Teichmüller Theory In Riemannian Geometry

Author : Anthony Tromba
Publisher : Birkhäuser
Page : 224 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886130

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Teichmüller Theory in Riemannian Geometry by Anthony Tromba Pdf

These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 888 pages
File Size : 47,5 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190558

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Author : Frederick P. Gardiner,Nikola Lakic
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 48,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821819838

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Quasiconformal Teichmüller Theory by Frederick P. Gardiner,Nikola Lakic Pdf

The Teichmuller space $T(X)$ is the space of marked conformal structures on a given quasi conformal surface $X$. This volume uses quasi conformal mapping to give a unified and up-to-date treatment of $T(X)$. Emphasis is placed on parts of the theory applicable to non compact surfaces and to surfaces possibly of infinite analytic type. The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to three-dimensional manifolds through its relationship to Kleinian groups, and to one-dimensional dynamics through its relationship to quasi symmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.

Author : R. C. Penner
Publisher : European Mathematical Society
Page : 388 pages
File Size : 47,6 Mb
Release : 2012
Category : Teichmu ller spaces
ISBN : 3037190752

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Decorated Teichmüller Theory by R. C. Penner Pdf

There is an essentially ``tinker-toy'' model of a trivial bundle over the classical Teichmuller space of a punctured surface, called the decorated Teichmuller space, where the fiber over a point is the space of all tuples of horocycles, one about each puncture. This model leads to an extension of the classical mapping class groups called the Ptolemy groupoids and to certain matrix models solving related enumerative problems, each of which has proved useful both in mathematics and in theoretical physics. These spaces enjoy several related parametrizations leading to a rich and intricate algebro-geometric structure tied to the already elaborate combinatorial structure of the tinker-toy model. Indeed, the natural coordinates give the prototypical examples not only of cluster algebras but also of tropicalization. This interplay of combinatorics and coordinates admits further manifestations, for example, in a Lie theory for homeomorphisms of the circle, in the geometry underlying the Gauss product, in profinite and pronilpotent geometry, in the combinatorics underlying conformal and topological quantum field theories, and in the geometry and combinatorics of macromolecules. This volume gives the story a wider context of these decorated Teichmuller spaces as developed by the author over the last two decades in a series of papers, some of them in collaboration. Sometimes correcting errors or typos, sometimes simplifying proofs, and sometimes articulating more general formulations than the original research papers, this volume is self contained and requires little formal background. Based on a master's course at Aarhus University, it gives the first treatment of these works in monographic form.

Author : M. Seppälä,T. Sorvali
Publisher : Elsevier
Page : 262 pages
File Size : 46,8 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080872808

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Geometry of Riemann Surfaces and Teichmüller Spaces by M. Seppälä,T. Sorvali Pdf

The moduli problem is to describe the structure of the space of isomorphism classes of Riemann surfaces of a given topological type. This space is known as the moduli space and has been at the center of pure mathematics for more than a hundred years. In spite of its age, this field still attracts a lot of attention, the smooth compact Riemann surfaces being simply complex projective algebraic curves. Therefore the moduli space of compact Riemann surfaces is also the moduli space of complex algebraic curves. This space lies on the intersection of many fields of mathematics and may be studied from many different points of view. The aim of this monograph is to present information about the structure of the moduli space using as concrete and elementary methods as possible. This simple approach leads to a rich theory and opens a new way of treating the moduli problem, putting new life into classical methods that were used in the study of moduli problems in the 1920s.

Author : Athanase Papadopoulos
Publisher : Erich Schmidt Verlag GmbH & Co. KG
Page : 844 pages
File Size : 51,5 Mb
Release : 2007
Category : Mathematics
ISBN : 3037191171

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

For several decades, Teichmuller theory has been one of the most active research areas in mathematics, with a very wide range of points of view, including Riemann surface theory, hyperbolic geometry, low-dimensional topology, several complex variables, algebraic geometry, arithmetic, partial differential equations, dynamical systems, representation theory, symplectic geometry, geometric group theory, and mathematical physics. This book is the fourth volume in a Handbook of Teichmuller Theory project that started as an attempt to present, in a most comprehensive and systematic way, the various aspects of this theory with its relations to all the fields mentioned. The handbook is addressed to researchers as well as graduate students. This volume is divided into five parts: Part A: The metric and the analytic theory Part B: Representation theory and generalized structures Part C: Dynamics Part D: The quantum theory Part E: Sources Parts A, B, and D are sequels to parts on the same theme in previous volumes. Part E contains the translation together with a commentary of an important paper by Teichmuller that is almost unknown, even to specialists. Making the original ideas of and motivations for a theory clear is crucial for many reasons, and making this translation, together with the commentary that follows, available will give readers a broader perspective on Teichmuller theory. The various volumes in this collection are written by experts who have a broad view on the subject. In general, the chapters are expository, while some of them contain new and important results.

Author : Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer
Publisher : Springer Nature
Page : 121 pages
File Size : 41,8 Mb
Release : 2020-08-19
Category : Mathematics
ISBN : 9783030552930

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Global Riemannian Geometry: Curvature and Topology by Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer Pdf

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.

Author : Junjiro Noguchi,Takeo Ohsawa
Publisher : Springer
Page : 0 pages
File Size : 51,7 Mb
Release : 1991-07-10
Category : Mathematics
ISBN : 3540540539

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Prospects in Complex Geometry by Junjiro Noguchi,Takeo Ohsawa Pdf

In the Teichmüller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years. Thus the central subject of "Complex Structure" was a timely choice for the joint meetings in Katata and Kyoto in 1989. The invited participants exchanged ideas on different approaches to related topics in complex geometry and mapped out the prospects for the next few years of research.

Author : Junjiro Noguchi,Takeo Ohsawa
Publisher : Springer
Page : 431 pages
File Size : 47,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540473701

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Prospects in Complex Geometry by Junjiro Noguchi,Takeo Ohsawa Pdf

In the Teichmüller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years. Thus the central subject of "Complex Structure" was a timely choice for the joint meetings in Katata and Kyoto in 1989. The invited participants exchanged ideas on different approaches to related topics in complex geometry and mapped out the prospects for the next few years of research.

Author : Jürgen Jost
Publisher : Springer
Page : 295 pages
File Size : 49,8 Mb
Release : 2014-03-12
Category : Mathematics
ISBN : 3662034476

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Compact Riemann Surfaces by Jürgen Jost Pdf

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Author : Ben Andrews,Christopher Hopper
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 51,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9783642162855

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The Ricci Flow in Riemannian Geometry by Ben Andrews,Christopher Hopper Pdf

This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.

Author : Huai-Dong Cao,Shing-Tung Yau
Publisher : Unknown
Page : 368 pages
File Size : 55,9 Mb
Release : 2008
Category : Geometry, Differential
ISBN : STANFORD:36105130567345

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Geometric Flows by Huai-Dong Cao,Shing-Tung Yau Pdf

Author : Scott A. Wolpert
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 45,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849866

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Families of Riemann Surfaces and Weil-Petersson Geometry by Scott A. Wolpert Pdf

Provides a generally self-contained course for graduate students and postgraduates on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. It also offers an update for researchers; material not otherwise found in a single reference is included; and aunified approach is provided for an array of results.

Author : Luther Pfahler Eisenhart
Publisher : Princeton University Press
Page : 320 pages
File Size : 40,9 Mb
Release : 2016-08-11
Category : Mathematics
ISBN : 9781400884216

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Riemannian Geometry by Luther Pfahler Eisenhart Pdf

In his classic work of geometry, Euclid focused on the properties of flat surfaces. In the age of exploration, mapmakers such as Mercator had to concern themselves with the properties of spherical surfaces. The study of curved surfaces, or non-Euclidean geometry, flowered in the late nineteenth century, as mathematicians such as Riemann increasingly questioned Euclid's parallel postulate, and by relaxing this constraint derived a wealth of new results. These seemingly abstract properties found immediate application in physics upon Einstein's introduction of the general theory of relativity. In this book, Eisenhart succinctly surveys the key concepts of Riemannian geometry, addressing mathematicians and theoretical physicists alike.

Author : Wilhelm Klingenberg
Publisher : Walter de Gruyter
Page : 430 pages
File Size : 41,8 Mb
Release : 1995
Category : Mathematics
ISBN : 3110145936

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Riemannian Geometry by Wilhelm Klingenberg Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)