Complex Manifolds And Hyperbolic Geometry

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Complex Manifolds and Hyperbolic Geometry

Author : Clifford J. Earle,Iberoamerican Congress on Geometry (2 : 2001 : Guanajuato),William J. Harvey,Sevín Recillas-Pishmish
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 54,5 Mb
Release : 2002
Category : Automorphic forms
ISBN : 9780821829578

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Complex Manifolds and Hyperbolic Geometry by Clifford J. Earle,Iberoamerican Congress on Geometry (2 : 2001 : Guanajuato),William J. Harvey,Sevín Recillas-Pishmish Pdf

This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigacion en Matematicas A.C., an internationally recognized program of research in pure mathematics. The conference topics were chosen with an eye toward the presentation of new methods, recent results, and the creation of more interconnections between the different research groups working in complex manifolds and hyperbolic geometry. This volume reflects both the unity and the diversity of these subjects. Researchers around the globe have been working on problems concerning Riemann surfaces, as well as a wide scope of other issues: the theory of Teichmuller spaces, theta functions, algebraic geometry and classical function theory. Included here are discussions revolving around questions of geometry that are related in one way or another to functions of a complex variable. There are contributors on Riemann surfaces, hyperbolic geometry, Teichmuller spaces, and quasiconformal maps. Complex geometry has many applications--triangulations of surfaces, combinatorics, ordinary differential equations, complex dynamics, and the geometry of special curves and jacobians, among others. In this book, research mathematicians in complex geometry, hyperbolic geometry and Teichmuller spaces will find a selection of strong papers by international experts.

Complex Hyperbolic Geometry

Author : William Mark Goldman
Publisher : Oxford University Press
Page : 342 pages
File Size : 40,8 Mb
Release : 1999
Category : Mathematics
ISBN : 019853793X

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Complex Hyperbolic Geometry by William Mark Goldman Pdf

This is the first comprehensive treatment of the geometry of complex hyperbolic space, a rich area of research with numerous connections to other branches of mathematics, including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie groups, and harmonic analysis.

Hyperbolic Manifolds

Author : Albert Marden
Publisher : Cambridge University Press
Page : 535 pages
File Size : 53,8 Mb
Release : 2016-02
Category : Mathematics
ISBN : 9781107116740

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Hyperbolic Manifolds by Albert Marden Pdf

This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.

Hyperbolic Manifolds and Discrete Groups

Author : Michael Kapovich
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 42,8 Mb
Release : 2009-08-04
Category : Mathematics
ISBN : 9780817649135

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Hyperbolic Manifolds and Discrete Groups by Michael Kapovich Pdf

Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the "Big Monster," i.e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.

Hyperbolic Manifolds and Holomorphic Mappings

Author : Shoshichi Kobayashi
Publisher : World Scientific
Page : 161 pages
File Size : 49,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812564962

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Hyperbolic Manifolds and Holomorphic Mappings by Shoshichi Kobayashi Pdf

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 Kleinian Groups

Author : Katsuhiko Matsuzaki,Masahiko Taniguchi
Publisher : Clarendon Press
Page : 265 pages
File Size : 43,7 Mb
Release : 1998-04-30
Category : Mathematics
ISBN : 9780191591204

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Hyperbolic Manifolds and Kleinian Groups by Katsuhiko Matsuzaki,Masahiko Taniguchi Pdf

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

Complex Manifolds without Potential Theory

Author : Shiing-shen Chern
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781468493443

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Complex Manifolds without Potential Theory by Shiing-shen Chern Pdf

From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#

Outer Circles

Author : A. Marden
Publisher : Cambridge University Press
Page : 393 pages
File Size : 46,9 Mb
Release : 2007-05-31
Category : Mathematics
ISBN : 9781139463768

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Outer Circles by A. Marden Pdf

We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

Complex Geometry

Author : G. Komatsu
Publisher : CRC Press
Page : 250 pages
File Size : 50,6 Mb
Release : 1992-11-19
Category : Mathematics
ISBN : 0824788184

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Complex Geometry by G. Komatsu Pdf

Presents the proceedings of an international conference on complex geometry and related topics, held in commemoration of the 50th anniversary of Osaka University, Osaka, Japan. The text focuses on the CR invariants, hyperbolic geometry, Yamabe-type problems, and harmonic maps.

Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

Author : Alexander Isaev
Publisher : Springer
Page : 149 pages
File Size : 48,7 Mb
Release : 2007-03-11
Category : Mathematics
ISBN : 9783540691532

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Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds by Alexander Isaev Pdf

In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.

Foundations of Hyperbolic Manifolds

Author : John Ratcliffe
Publisher : Springer Science & Business Media
Page : 761 pages
File Size : 41,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475740134

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Foundations of Hyperbolic Manifolds by John Ratcliffe Pdf

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

Complex Hyperbolic Geometry

Author : William M. Goldman
Publisher : Unknown
Page : 212 pages
File Size : 40,5 Mb
Release : 1992
Category : Electronic
ISBN : OCLC:638043754

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Complex Hyperbolic Geometry by William M. Goldman Pdf

Hyperbolic Complex Spaces

Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662035825

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Hyperbolic Complex Spaces by Shoshichi Kobayashi Pdf

In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.

Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday

Author : Toshiki Mabuchi,J Noguchi,T Ochiai
Publisher : World Scientific
Page : 261 pages
File Size : 55,8 Mb
Release : 1994-12-09
Category : Mathematics
ISBN : 9789814501224

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Geometry And Analysis On Complex Manifolds: Festschrift For S Kobayashi's 60th Birthday by Toshiki Mabuchi,J Noguchi,T Ochiai Pdf

This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein-Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

Complex Manifolds

Author : James A. Morrow,Kunihiko Kodaira
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 45,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821840559

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Complex Manifolds by James A. Morrow,Kunihiko Kodaira Pdf

Serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, this book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Kahler manifolds called Hodge manifolds is algebraic.