Kichoon Yang - Böcker

'Et moi, ..., si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non- 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

tEl moi, "0, si j'avait su comment en revenir, je One service mathematics has rendered the n 'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlinea- ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other s- ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One s- vice topology has rendered mathematical physics ...'; 'One service logic has rendered computer science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

This monograph is based on the idea that the study of complete minimal surfaces in RXX of finite total curvature amounts to the study of linear series on algebraic curves. A detailed account of the Puncture Number Problem, which seeks to determine all possible underlying conformal structures for immersed complete minimal surfaces of finite total curvature, is given here. Several recent results on the puncture number problem are given along with numerous examples. The emphasis is on manufacturing minimal surfaces from a given Riemann surface using the theory of divisions and residue calculus. Relevant results from algebraic geometry are collected in Chapter 1, which makes the book nearly self-contained. A brief survey of minimal surface theory in general is given in Chapter 2. Chapter 3 includes Mo's recent moduli construction. This text should interest graduate students and research mathematicians in differential geometry, function theory and algebraic curves, as well as for those working in materials science or crystallography.

The main purpose of this volume is to give an exposition of various aspects of meromorphic functions and linear series on algebraic curves, with some emphasis on families of meromorphic functions. It is written in such a way as to facilitate their applications in other areas of mathematics. Meromorphic functions on a compact Riemann surface, or, more generally, holomorphic curves and linear series, have numerous applications in many different areas of mathematics. This work gives a concise survey of results in the elementary theory of meromorphic functions and divisors on curves, and makes these results more accessible to students and non-experts, in particular differential geometers. This volume should be of interest to graduate students and researchers in mathematics, especially in algebraic and differential geometry.

tEl moi, "0, si j'avait su comment en revenir, je One service mathematics has rendered the n 'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlinea- ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other s- ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One s- vice topology has rendered mathematical physics ...'; 'One service logic has rendered computer science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

This monograph is based on the idea that the study of complete minimal surfaces in R3 of finite total curvature amounts to the study of linear series on algebraic curves. A detailed account of the Puncture Number Problem, which seeks to determine all possible underlying conformal structures for immersed complete minimal surfaces of finite total curvature, is given here for the first time in book form. Several recent results on the puncture number problem are given along with numerous examples. The emphasis is on manufacturing minimal surfaces from a given Riemann surface using the theory of divisions and residue calculus. Relevant results from algebraic geometry are collected in Chapter 1, which makes the book nearly self-contained. A brief survey of minimal surface theory in general is given in Chapter 2. Chapter 3 includes Mo's recent moduli construction. For graduate students and research mathematicians in differential geometry, function theory and algebraic curves, as well as for those working in materials science or crystallography.

The main purpose of this volume is to give an exposition of various aspects of meromorphic functions and linear series on algebraic curves, with some emphasis on families of meromorphic functions. It is written in such a wayas to facilitate their applications in other areas of mathematics. Meromorphic functions on a compact Riemann surface, or, more generally, holomorphic curves and linear series, have numerous applications in many different areas of mathematics. This work gives a concise survey of results in the elementary theory of meromorphic functions and divisors on curves, and makes these results more accessible to students and non-experts, in particular differential geometers. Audience: This volume will be of interest to graduate students and researchers in mathematics, especially in algebraic and differential geometry.

'Et moi, ..., si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non- 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.