Aspects of Mathematics – serie

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Del 36 - Aspects of Mathematics
Frobenius Manifolds
Quantum Cohomology and Singularities
AvClaus Hertling,Matilde Marcolli
Häftad, Engelska, 2012
1 192 kr
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Frobenius Mannigfaltigkeiten - ein aktuelles Gebiet, das Algebraische Geometrie und Quanten Kohomologie verbindet, motiviert wurde es durch die Physik. Dieses Buch ist augenblicklich das einzige, das alle wichtigen Experten zusammenbringt und die verschieden thematischen Schwerpunkte zusammenstellt, es gibt einen hervorragenden Überblick über "the state of the art" dieses Forschungsgebietes.
Del 27 - Aspects of Mathematics
Lie Group Actions in Complex Analysis
AvDimitrij Akhiezer
Häftad, Engelska, 2011
492 kr
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This book was planned as an introduction to a vast area, where many contri butions have been made in recent years. The choice of material is based on my understanding of the role of Lie groups in complex analysis. On the one hand, they appear as the automorphism groups of certain complex spaces, e. g. , bounded domains in en or compact spaces, and are therefore important as being one of their invariants. On the other hand, complex Lie groups and, more generally, homoge neous complex manifolds, serve as a proving ground, where it is often possible to accomplish a task and get an explicit answer. One good example of this kind is the theory of homogeneous vector bundles over flag manifolds. Another example is the way the global analytic properties of homogeneous manifolds are translated into algebraic language. It is my pleasant duty to thank A. L. Onishchik, who first introduced me to the theory of Lie groups more than 25 years ago. I am greatly indebted to him and to E. B. Vinberg forthe help and advice they have given me for years. I would like to express my gratitude to M. Brion, B. GilIigan, P. Heinzner, A. Hu kleberry, and E. Oeljeklaus for valuable discussions of various subjects treated here. A part of this book was written during my stay at the Ruhr-Universitat Bochum in 1993. I thank the Deutsche Forschungsgemeinschaft for its research support and the colleagues in Bochum for their hospitality.
Del 21 - Aspects of Mathematics
Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm
AvHirotaka Fujimoto
Häftad, Engelska, 2013
546 kr
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This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other hand. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, but also for those, who intend to do further research on minimal surfaces.
Del 28 - Aspects of Mathematics
Singular Nonlinear Partial Differential Equations
AvRaymond Gérard,Hidetoshi Taharam. fl.
Häftad, Engelska, 2011
1 085 kr
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The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations. We study the existence of formal power series solutions, holomorphic solutions, and singular solutions of singular non linear partial differential equations. In the first chapter, we introduce operators with regular singularities in the one variable case and we give a new simple proof of the classical Maillet's theorem for algebraic differential equations. In chapter 2, we extend this theory to operators in several variables. The chapter 3 is devoted to the study of formal and convergent power series solutions of a class of singular partial differential equations having a linear part, using the method of iteration and also Newton's method. As an appli cation of the former results, we look in chapter 4 at the local theory of differential equations of the form xy' = 1(x,y) and, in particular, we show how easy it is to find the classical results on such an equation when 1(0,0) = 0 and give also the study of such an equation when 1(0,0) #- 0 which was never given before and can be extended to equations of the form Ty = F(x, y) where T is an arbitrary vector field.
Del 6 - Aspects of Mathematics
Rational Points
Seminar Bonn/Wuppertal 1983/84
AvGerd Faltings,Gisbert Wüstholz
Häftad, Engelska, 2013
546 kr
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This book consists of the notes from the seminar Bonn/ Wuppertal 1983/ 84 on Arithmetic Geometry. It contains a proof for the Mordell conjecture and may be useful as an introduction to Arakelov's point of view in diophantine geometry. The third edition includes an appendix in which a detailed survey on the spectacular recent developments in arithmetic algebraic geometry is given. These beautiful new results have their roots in the material covered by this book.
Del 10 - Aspects of Mathematics
Seminar on New Results in Nonlinear Partial Differential Equations
A Publication of the Max-Planck-Institut für Mathematik, Bonn
AvAnthony Tromba,Friedrich Hirzebruch
Häftad, Engelska, 2012
1 085 kr
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This book consists almost entirely of papers delivered at the Seminar on partial differential equations held at Max-Planck-Institut in the spring of 1984. They give an insight into important recent research activities. Some further developments are also included.
Complex Analysis
Proceedings of the International Workshop Wuppertal 1990
AvKlas Diederich
Häftad, Engelska, 2012
1 085 kr
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This volume contains the Proceedings of the International Workshop "Complex Analysis", which was held from February 12-16, 1990, in Wuppertal (Germany) in honour of H. Grauert, one of the most creative mathematicians in Complex Analysis of this century. In complete accordance with the width of the work of Grauert the book contains research notes and longer articles of many important mathematicians from all areas of Complex Analysis (Altogether there a re 49 articles in the volume). Some of the main subjects are: Cau chy-Riemann Equations with estimates, q-convexity, CR structures, deformation theory, envelopes of holomorphy, function algebras, complex group actions, Hodge theory, instantons, Kahler geometry, Lefschetz theorems, holomorphic mappings, Nevanlinna theory, com plex singularities, twistor theory, uniformization.
Del 16 - Aspects of Mathematics
From Gauss to Painlevé
A Modern Theory of Special Functions
AvKatsunori Iwasaki,Hironobu Kimuram. fl.
Häftad, Engelska, 2012
1 516 kr
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Preface The Gamma function, the zeta function, the theta function, the hyper geometric function, the Bessel function, the Hermite function and the Airy function, . . . are instances of what one calls special functions. These have been studied in great detail. Each of them is brought to light at the right epoch according to both mathematicians and physicists. Note that except for the first three, each of these functions is a solution of a linear ordinary differential equation with rational coefficients which has the same name as the functions. For example, the Bessel equation is the simplest non-trivial linear ordinary differential equation with an irreg ular singularity which leads to the theory of asymptotic expansion, and the Bessel function is used to describe the motion of planets (Kepler's equation). Many specialists believe that during the 21st century the Painleve functions will become new members of the community of special func tions. For any case, mathematics and physics nowadays already need these functions. The corresponding differential equations are non-linear ordinary differential equations found by P. Painleve in 1900 fqr purely mathematical reasons. It was only 70 years later that they were used in physics in order to describe the correlation function of the two dimen sional Ising model. During the last 15 years, more and more people have become interested in these equations, and nice algebraic, geometric and analytic properties were found.
Del 32 - Aspects of Mathematics
Hypergeometric Functions, My Love
Modular Interpretations of Configuration Spaces
AvMasaaki Yoshida
Häftad, Engelska, 2013
815 kr
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Die klassische Geschichte der hypergeometrischen Funktionen, dem Raum der Konfigurationen von 4 Punkten auf der projektiven Geraden, elliptischen Kurven, Modulfunktionen und Theta Funktionen, wird in diesem Buch zur Geschichte der hypergeometrischen Funktionen in 4 Variablen, dem Raum der Konfigurationen von 6 Punkten in der projektiven Ebene, K3 Flächen, Theta Funktionen in 4 Variablen weiterentwickelt. Der Autor erzählt die Geschichte in einem lebendigen Stil, beginnend von einem elementaren Niveau, so daß Studenten angesprochen werden.
Del 29 - Aspects of Mathematics
Ball and Surface Arithmetics
AvRolf-Peter Holzapfel
Häftad, Engelska, 2012
546 kr
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This monograph is based on the work of the author on surface theory con nected with ball uniformizations and arithmetic ball lattices during several years appearing in a lot of special articles. The first four chapters present the heart of this work in a self-contained manner (up to well-known ba sic facts) increased by the new functorial concept of orbital heights living on orbital surfaces. It is extended in chapter 6 to an explicit HURWITZ theory for CHERN numbers of complex algebraic surfaces with the mildest singularities, which are necessary for general application and proofs. The chapter 5 is dedicated to the application of results in earlier chapters to rough and fine classifications of PICARD modular surfaces. For this part we need additionally the arithmetic work of FEUSTEL whose final results are presented without proofs but with complete references. We had help ful connections with Russian mathematicians around VENKOV, VINBERG, MANIN, SHAFAREVICH and the nice guide line of investigations of HILBERT modular surfaces started by HIRZEBRUCH in Bonn. More recently, we can refer to the independent (until now) study of Zeta functions of PICARD modular surfaces in the book [L-R] edited by LANGLANDS and RAMAKR ISHN AN. The basic idea of introducing arrangements on surfaces comes from the monograph [BHH], (BARTHEL, HOFER, HIRZEBRUCH) where linear ar rangements on the complex projective plane ]p2 play the main role.
Del 33 - Aspects of Mathematics
Moduli of Curves and Abelian Varieties
The Dutch Intercity Seminar on Moduli
AvCarel Faber,Eduard Looijenga
Häftad, Engelska, 2012
546 kr
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The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Rain, E. Looijenga, and F. Oort, originates from the Dutch Intercity Seminar on Moduli (year 1995-96). Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles. Topics include a stratification of a moduli space of abelian varieties in positive characteristic, and the calculation of the classes of the strata, tautological classes for moduli of abelian varieties as well as for moduli of curves, correspondences between moduli spaces of curves, locally symmetric families of curves and jaco bians, and the role of symmetric product spaces in quantum field theory, string theory and matrix theory. This Intercity Seminar is part of the long term project "Algebraic curves and Riemann surfaces: geometry, arithmetic and applications" , sponsored hy the Netherlands Organization for Scientific Research (NWO), that has been running since 1994. Its ancestry can be traced back to joint activities in the seventies (if not earlier), which as of 1980 had evolved into active biweekly research seminars. These have been a focal point of Dutch algebraic geometry and singularity theory since. We are grateful to NWO for its support for the project. C.F. thanks the Max-Planck-Institut fur Mathematik, Bonn, for support during the final stages of the preparation of this volume.
Del 5 - Aspects of Mathematics
Automorphic Forms and the Picard Number of an Elliptic Surface
AvPeter F. Stiller
Häftad, Engelska, 2012
546 kr
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In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E,Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E,E) which is of I type (1,1), that is to say a class in H(E,9!) which can be viewed as a 2 subspace of H(E,E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p,p) is algebraic. In our case this is the Lefschetz Theorem on (I,l)-classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E,Z) for 2 its image under the natural mapping into H (E,t). Thus NS(E) modulo 2 torsion is Hl(E,n!) n H(E,Z) and th 1 b i f h -~ p measures e a ge ra c part 0 t e cohomology.
Del 34 - Aspects of Mathematics
Cauchy-Riemann Complex
Integral Formulae and Neumann Problem
AvIngo Lieb,Joachim Michel
Häftad, Engelska, 2012
546 kr
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This book presents complex analysis of several variables from the point of view of the Cauchy-Riemann equations and integral representations. A more detailed description of our methods and main results can be found in the introduction. Here we only make some remarks on our aims and on the required background knowledge. Integral representation methods serve a twofold purpose: 1° they yield regularity results not easily obtained by other methods and 2°, along the way, they lead to a fairly simple development of parts of the classical theory of several complex variables. We try to reach both aims. Thus, the first three to four chapters, if complemented by an elementary chapter on holomorphic functions, can be used by a lecturer as an introductory course to com plex analysis. They contain standard applications of the Bochner-Martinelli-Koppelman integral representation, a complete presentation of Cauchy-Fantappie forms giving also the numerical constants of the theory, and a direct study of the Cauchy-Riemann com plex on strictly pseudoconvex domains leading, among other things, to a rather elementary solution of Levi's problem in complex number space en. Chapter IV carries the theory from domains in en to strictly pseudoconvex subdomains of arbitrary - not necessarily Stein - manifolds. We develop this theory taking as a model classical Hodge theory on compact Riemannian manifolds; the relation between a parametrix for the real Laplacian and the generalised Bochner-Martinelli-Koppelman formula is crucial for the success of the method.
Del 22 - Aspects of Mathematics
Riemann-Hilbert Problem
A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev
AvD. V. Anosov,A. A. Bolibruch
Häftad, Engelska, 2014
923 kr
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This book is devoted to Hilbert's 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concems the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this tumed out to be a rare case of a wrong forecast made by hirn. In 1989 the second author (A.B.) discovered a counterexample, thus 1 obtaining a negative solution to Hilbert's 21st problem. After we recognized that some "data" (singularities and monodromy) can be obtai ned from a Fuchsian system and some others cannot, we are enforced to change our point of view. To make the terminology more precise, we shaII caII the foIIowing problem the Riemann-Hilbert problem for such and such data: does there exist a Fuchsian system having these singularities and monodromy? The contemporary version of the 21 st Hilbert problem is to find conditions implying a positive or negative solution to the Riemann-Hilbert problem.
Introduction to the Geometry of Foliations, Part A
Foliations on Compact Surfaces, Fundamentals for Arbitrary Codimension, and Holonomy
AvGilbert Hector,Ulrich Hirsch
Häftad, Tyska, 2012
561 kr
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Del 25 - Aspects of Mathematics
Algebraic Geometry and its Applications
Proceedings of the 8th Algebraic Geometry Conference, Yaroslavl’ 1992. A Publication from the Steklov Institute of Mathematics. Adviser: Armen Sergeev
AvAlexander Tikhomirov,Andrej Tyurin
Häftad, Engelska, 2012
546 kr
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This volume consists of articles presented as talks at the Algebraic Geometry Conference held in the State Pedagogical Institute of Yaroslavl'from August 10 to 14, 1992. These conferences in Yaroslavl' have become traditional in the former USSR, now in Russia, since January 1979, and are held at least every two years. The present conference, the eighth one, was the first in which several foreign mathematicians participated. From the Russian side, 36 specialists in algebraic geometry and related fields (invariant theory, topology of manifolds, theory of categories, mathematical physics etc. ) were present. As well modern directions in algebraic geometry, such as the theory of exceptional bundles and helices on algebraic varieties, moduli of vector bundles on algebraic surfaces with applications to Donaldson's theory, geometry of Hilbert schemes of points, twistor spaces and applications to string theory, as more traditional areas, such as birational geometry of manifolds, adjunction theory, Hodge theory, problems of rationality in the invariant theory, topology of complex algebraic varieties and others were represented in the lectures of the conference. In the following we will give a brief sketch of the contents of the volume. In the paper of W. L. Baily three problems of algebro-geometric nature are posed. They are connected with hermitian symmetric tube domains. In particular, the 27-dimensional tube domain 'Fe is treated, on which a certain real form of E7 acts, which contains a "nice" arithmetic subgroup r e, as observed earlier by W. Baily.
G-Functions and Geometry
A Publication of the Max-Planck-Institut für Mathematik, Bonn
AvYves André
Häftad, Tyska, 1989
662 kr
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Existenz semiuniverseller Deformationen in der komplexen Analysis
AvHarald Stieber
Häftad, Tyska, 1988
561 kr
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Capacities in Complex Analysis
AvUrban Cegrell
Häftad, Tyska, 1988
561 kr
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Manifolds and Modular Forms
AvFriedrich Hirzebruch
Häftad, Tyska, 1992
762 kr
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Del 18 - Aspects of Mathematics
Conjectures in Arithmetic Algebraic Geometry
A Survey
AvWilfred W. J. Hulsbergen
Häftad, Engelska, 1992
546 kr
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Harmonic Maps and Integrable Systems
AvJohn C. Wood
Häftad, Tyska, 1994
611 kr
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Harmonic maps are maps between Riemannian or pseudo-Riemannian manifolds which extremize a natural energy integral. They have found many applications, for example, to the theory of minimal and constant mean curvature suface. In physics they arise as the non-linear sigma and chiral models of particle physics. Recently, there has been an explosion of interest in applying the methods to ingrable systems to find and study harmonic maps. Bringing together experts in the field of harmonic maps and integrable systems to give a coherent account of this subject, this book starts with introductory articles, so that the book is self-contained. It should be of interest to graduate students and researchers interested in applying integrable systems to variational problems, and could form the basis of a graduate course.
Contributions to Complex Analysis and Analytic Geometry
Dedicated to Pierre Dolbeault
AvHenri Skoda,Jean-Marie Trépreau
Häftad, Tyska, 1994
561 kr
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This volume is drawn from the "Colloque en l'honneur de Pierre Dolbeault", which was organized in June 1992 at the "Universite de Paris IV". It contains a description of the scientific life and achievements of Pierre Dolbeault by Pierre Lelong, V. Ancona, B. Gaveau, B. Berndtsson, E.M. Chirka, E.L. Stout, J.P. Demailly, K. Diederich, G. Herbort, P. Dolbeault, G. Henkin, A. Huckleberry, M. Passare, A. Tsikh, O. Zhdanov and B. Shiffman. Most of the articles combine a survey of the situation of a certain field with the exposition of new research results by the authors. The subjects range from Riemann surfaces with boundary embedded in CPn over co-homology of complex spaces, meromorphic maps, residues, regularization of closed positive currents and homogenous manifolds to CR-geometry, pseudoconvex domains of finite type, and estimates for the Cauchy-Riemann equations. Thus, the volume presents a broad variety of modern research in complex analysis.
Wittrings
AvManfred Knebusch,Manfred Kolster
Häftad, Tyska, 1982
510 kr
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Del 1 - Aspects of Mathematics
Geometrische Methoden in der Invariantentheorie
AvHanspeter Kraft
Häftad, Tyska, 1984
662 kr
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Introduction to the Geometry of Foliations, Part B
Foliations of Codimension One
AvGilbert Hector
Häftad, Tyska, 1983
561 kr
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Elliptic Curves over Number Fields with Prescribed Reduction Type
AvMichael Laska
Häftad, Tyska, 1983
561 kr
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Equations of Navier-Stokes and Abstract Parabolic Equations
AvWolf von Wahl
Häftad, Tyska, 1985
561 kr
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Lectures on the Mordell-Weil Theorem
AvJean Pierre Serre
Häftad, Tyska, 1989
762 kr
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Fuchsian Differential Equations
With Special Emphasis on the Gauss-Schwarz Theory
AvMasaaki Yoshida
Häftad, Tyska, 1987
662 kr
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Aspects of Mathematics – serie

Frobenius Manifolds

Lie Group Actions in Complex Analysis

Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm

Singular Nonlinear Partial Differential Equations

Rational Points

Seminar on New Results in Nonlinear Partial Differential Equations

Complex Analysis

From Gauss to Painlevé

Hypergeometric Functions, My Love

Ball and Surface Arithmetics

Moduli of Curves and Abelian Varieties

Automorphic Forms and the Picard Number of an Elliptic Surface

Cauchy-Riemann Complex

Riemann-Hilbert Problem

Introduction to the Geometry of Foliations, Part A

Algebraic Geometry and its Applications

G-Functions and Geometry

Existenz semiuniverseller Deformationen in der komplexen Analysis

Capacities in Complex Analysis

Manifolds and Modular Forms

Conjectures in Arithmetic Algebraic Geometry

Harmonic Maps and Integrable Systems

Contributions to Complex Analysis and Analytic Geometry

Wittrings

Geometrische Methoden in der Invariantentheorie

Introduction to the Geometry of Foliations, Part B

Elliptic Curves over Number Fields with Prescribed Reduction Type

Equations of Navier-Stokes and Abstract Parabolic Equations

Lectures on the Mordell-Weil Theorem

Fuchsian Differential Equations