Hyperbolic Manifolds And Holomorphic Mappings
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Hyperbolic Manifolds And Holomorphic Mappings
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Author : Shoshichi Kobayashi
language : en
Publisher: World Scientific
Release Date : 2005
Hyperbolic Manifolds And Holomorphic Mappings written by Shoshichi Kobayashi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections ?invariant metrics and pseudo-distances? and ?hyperbolic complex manifolds? within the section ?holomorphic mappings?. The invariant distance introduced in the first edition is now called the ?Kobayashi distance?, and the hyperbolicity in the sense of this book is called the ?Kobayashi hyperbolicity? to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
Hyperbolic Manifolds And Holomorphic Mappings
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Author : Shoshichi Kobayashi
language : en
Publisher:
Release Date : 1970
Hyperbolic Manifolds And Holomorphic Mappings written by Shoshichi Kobayashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Hyperbolic Manifolds And Holomorphic Mappings An Introduction Second Edition
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Author : Shoshichi Kobayashi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-11-02
Hyperbolic Manifolds And Holomorphic Mappings An Introduction Second Edition written by Shoshichi Kobayashi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-02 with Mathematics categories.
The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
Hyperbolic Manifolds And Holomorphic Mappings
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Author : Shōshichi Kobayashi
language : en
Publisher:
Release Date : 1987
Hyperbolic Manifolds And Holomorphic Mappings written by Shōshichi Kobayashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Complex manifolds categories.
Hyperbolic Manifolds And Holomorphic Mappings Kobayashi
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Author : Shoshichi Kobayashi
language : es
Publisher:
Release Date : 1970
Hyperbolic Manifolds And Holomorphic Mappings Kobayashi written by Shoshichi Kobayashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Intrinsic Measures On Complex Manifolds And Holomorphic Mappings
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Author : Donald A. Eisenman
language : en
Publisher: American Mathematical Soc.
Release Date : 1970
Intrinsic Measures On Complex Manifolds And Holomorphic Mappings written by Donald A. Eisenman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Analytic functions categories.
Minimal Surfaces From A Complex Analytic Viewpoint
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Author : Antonio Alarcón
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Minimal Surfaces From A Complex Analytic Viewpoint written by Antonio Alarcón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Harmonic Maps Between Riemannian Polyhedra
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Author : James Eells
language : en
Publisher: Cambridge University Press
Release Date : 2001-07-30
Harmonic Maps Between Riemannian Polyhedra written by James Eells and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-30 with Mathematics categories.
Harmonic maps between smooth Riemannian manifolds play a ubiquitous role in differential geometry. Examples include geodesics viewed as maps, minimal surfaces, holomorphic maps and Abelian integrals viewed as maps to a circle. The theory of such maps has been extensively developed over the last 40 years, and has significant applications throughout mathematics. This 2001 book extends that theory in full detail to harmonic maps between broad classes of singular Riemannian polyhedra, with many examples being given. The analytical foundation is based on existence and regularity results which use the potential theory of Riemannian polyhedral domains viewed as Brelot harmonic spaces and geodesic space targets in the sense of Alexandrov and Busemann. The work sets out much material on harmonic maps between singular spaces and will hence serve as a concise source for all researchers working in related fields.
The Geometric Theory Of Complex Variables
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Author : Peter V. Dovbush
language : en
Publisher: Springer Nature
Release Date : 2025-01-28
The Geometric Theory Of Complex Variables written by Peter V. Dovbush and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-28 with Mathematics categories.
This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.
Invariant Distances And Metrics In Complex Analysis
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Author : Marek Jarnicki
language : en
Publisher: Walter de Gruyter
Release Date : 2013-06-26
Invariant Distances And Metrics In Complex Analysis written by Marek Jarnicki and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-26 with Mathematics categories.
As in the field of "Invariant Distances and Metrics in Complex Analysis" there was and is a continuous progress this is now the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other metrics. The book considers only domains in Cn and assumes a basic knowledge of several complex variables. It is a valuable reference work for the expert but is also accessible to readers who are knowledgeable about several complex variables. Each chapter starts with a brief summary of its contents and continues with a short introduction. It ends with an "Exercises" and a "List of problems" section that gathers all the problems from the chapter. The authors have been highly successful in giving a rigorous but readable account of the main lines of development in this area.