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Complex Kleinian Groups

Complex Kleinian Groups
Author: Angel Cano
Publisher: Springer Science & Business Media
ISBN: 3034804814
Size: 34.84 MB
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This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.​
Complex Kleinian Groups
Language: en
Pages: 272
Authors: Angel Cano, Juan Pablo Navarrete, José Seade
Categories: Mathematics
Type: BOOK - Published: 2012-11-05 - Publisher: Springer Science & Business Media
This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be
Hyperbolic Manifolds and Kleinian Groups
Language: en
Pages: 264
Authors: Katsuhiko Matsuzaki, Masahiko Taniguchi
Categories: Mathematics
Type: BOOK - Published: 1998-04-30 - Publisher: Clarendon Press
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
Complex Hyperbolic Kleinian Groups
Language: en
Pages: 22
Authors: William Mark Goldman
Categories: Kleinian groups
Type: BOOK - Published: 1991 - Publisher:
Abstract: "Complex hyperbolic manifolds furnish the simplest examples of: (i) negatively curved Kähler manifolds and (ii) negatively curved Riemannian manifolds not having constant curvature. Their central importance is underscored by their appearance as the prototype of moduli spaces of various kinds of geometric structures. This paper surveys an ongoing project
Geometry, Groups and Dynamics
Language: en
Pages: 369
Authors: C. S. Aravinda, William M. Goldman, Krishnendu Gongopadhyay, Alexander Lubotzky, Mahan Mj, Anthony Weaver
Categories: Discrete groups
Type: BOOK - Published: 2015-05-01 - Publisher: American Mathematical Soc.
This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of
Laminations and Foliations in Dynamics, Geometry and Topology
Language: en
Pages: 233
Authors: Mikhail Lyubich, John Willard Milnor
Categories: Mathematics
Type: BOOK - Published: 2001 - Publisher: American Mathematical Soc.
This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research
Conformal Graph Directed Markov Systems on Carnot Groups
Language: en
Pages: 153
Authors: Vasileios Chousionis, Jeremy T. Tyson, Mariusz Urbanski
Categories: Mathematics
Type: BOOK - Published: 2020-09-28 - Publisher: American Mathematical Soc.
The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by
Nonlinear Dynamics New Directions
Language: en
Pages: 219
Authors: Hernán González-Aguilar, Edgardo Ugalde
Categories: Technology & Engineering
Type: BOOK - Published: 2015-03-09 - Publisher: Springer
This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well
Kleinian Groups and Hyperbolic 3-Manifolds
Language: en
Pages:
Authors: Y. Komori, V. Markovic, C. Series
Categories: Mathematics
Type: BOOK - Published: 2003-11-10 - Publisher: Cambridge University Press
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the proof
Some Theorems in Kleinian Groups and Complex Dynamics
Language: en
Pages: 65
Authors: Yan Mary He
Categories: Mathematics
Type: BOOK - Published: 2018 - Publisher:
This thesis is an amalgam of the two manuscripts [16] and [17] that the author completed during her graduate studies at the University of Chicago. Article [16] was published in Ergodic Theory and Dynamical Systems and is reprinted with permission here.
Kleinian Groups and Uniformization in Examples and Problems
Language: en
Pages: 198
Authors: Samuil Leĭbovich Krushkalʹ, Boris Nikolaevich Apanasov, Nikolaĭ Aleksandrovich Gusevskiĭ
Categories: Mathematics
Type: BOOK - Published: 1986 - Publisher: American Mathematical Soc.
Aimed at researchers, graduate students and undergraduates alike, this book presents a unified exposition of all the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. The past 20 years have seen a rejuvenation of the field, due to the development of