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6 produkter
6 produkter
856 kr
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Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general settings; abstract Sobolev space theories have been instrumental in this development. The purpose of this book is to communicate some of the recent work in the area while preparing the reader to study more substantial, related articles. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is relatively recent and appears for the first time in book format. There are plenty of exercises. The book is well suited for self-study, or as a text in a graduate course or seminar.The material is relevant to anyone who is interested in analysis and geometry in nonsmooth settings.
Quasiconformal Mappings and Analysis
A Collection of Papers Honoring F.W. Gehring
Inbunden, Engelska, 1997
1 068 kr
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This book comprises a broad selection of expository articles that were written in conjunction with an international conference held to honor F.W. Gehring on the occasion of his 70th birthday. The objective of both the symposium and the present volume was to survey a wide array of topics related to Gehring's fundamental research in the field of quasiconformal mappings, emphasizing the relation of these mappings to other areas of analysis. The book begins with a short biographical sketch and an overview of Gehring's mathematical achievements, including a complete list of his publications. This is followed by Olli Lehto's account of Gehring's career-long involvement with the Finnish mathematical community and his role in the evolution of the Finnish school of quasiconformal mapping. The remaining articles, written by prominent authorities in diverse branches of analysis, are arranged alphabetically. The principal speakers at the symposium were: Astala, Baernstein Earle, Jones, Kra, Lehto, Martin, Sullivan, and Va"isa"la".Other individuals, some unable to attend the conference, were invited to contribute articles to the volume, which should give readers new insights into numerous aspects of quasiconformal mappings and their applications to other fields of mathematical analysis. Friends and colleagues of Professor Gehring will be especially interested in the personal accounts of his mathematical career and the descriptions of his many important research contributions.
215 kr
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Del 27 - New Mathematical Monographs
Sobolev Spaces on Metric Measure Spaces
An Approach Based on Upper Gradients
Inbunden, Engelska, 2015
1 801 kr
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Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincaré inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincaré inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincaré inequalities under Gromov-Hausdorff convergence, and the Keith-Zhong self-improvement theorem for Poincaré inequalities.
612 kr
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Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general settings; abstract Sobolev space theories have been instrumental in this development. The purpose of this book is to communicate some of the recent work in the area while preparing the reader to study more substantial, related articles. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is relatively recent and appears for the first time in book format. There are plenty of exercises. The book is well suited for self-study, or as a text in a graduate course or seminar. The material is relevant to anyone who is interested in analysis and geometry in nonsmooth settings.
Quasiconformal Mappings and Analysis
A Collection of Papers Honoring F.W. Gehring
Häftad, Engelska, 2012
1 068 kr
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In August 1995 an international symposium on "Quasiconformal Mappings and Analysis" was held in Ann Arbor on the occasion of Professor Fred- erick W. Gehring's 70th birthday and his impending retirement from the Mathematics Department at the University of Michigan. The concept of the symposium was to feature broad survey talks on a wide array of topics related to Gehring's basic research contributions in the field of quasicon- formal mappings, emphasizing their relations to other parts of analysis. Principal speakers were Kari Astala, Albert Baernstein, Clifford Earle, Pe- ter Jones, Irwin Kra, OUi Lehto, Gaven Martin, Dennis Sullivan, and Jussi Vaisala. Financial support was provided by the National Science Founda- tion, with additional grants from the University of Michigan and from the Institute for Mathematics and its Applications. The symposium was a great success. The speakers rose to the occasion and presented excellent survey lectures. The present volume was conceived as a means for disseminating those expositions to a wider audience. Ad- ditional mathematicians, some of whom had not been able to attend the symposium, were invited to contribute similar articles.The result is a fit- ting tribute to Fred Gehring's pre-eminent role in developing the theory of quasiconformal mappings, through his own research and writings and lec- tures, and through his supervision of graduate students. The volume begins with descriptions of Gehring's mathematical career and an overview of his research achievements.