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Author : Irwin Kra,Bernard Maskit
Publisher : Princeton University Press
Page : 536 pages
File Size : 40,7 Mb
Release : 1981-05-21
Category : Mathematics
ISBN : 0691082677
Annotation The description for this book, Riemann SurfaceseRelated Topics (AM-97): Proceedings of the 1978 Stony Brook Conference. (AM-97), will be forthcoming.
Author : Irwin Kra,Bernard Maskit
Publisher : Unknown
Page : 128 pages
File Size : 55,8 Mb
Release : 2016
Category : MATHEMATICS
ISBN : OCLC:1248695521
The description for this book, Riemann Surfaces Related Topics (AM-97), Volume 97: Proceedings of the 1978 Stony Brook Conference. (AM-97), will be forthcoming.
Author : Irwin Kra,Bernard Maskit
Publisher : Princeton University Press
Page : 533 pages
File Size : 48,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881550
A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.
Author : Conference on Riemann Surfaces and Related Topics Staff
Publisher : Unknown
Page : 528 pages
File Size : 53,6 Mb
Release : 1981-01-01
Category : Electronic
ISBN : 0608064998
Author : Frederick P. Gardiner,Nikola Lakic
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 50,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821819838
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 : Yukio Matsumoto,José María Montesinos-Amilibia
Publisher : Springer
Page : 240 pages
File Size : 47,7 Mb
Release : 2011-08-17
Category : Mathematics
ISBN : 9783642225345
The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.
Author : Arielle Leitner,Federico Vigolo
Publisher : Springer Nature
Page : 249 pages
File Size : 50,5 Mb
Release : 2024-01-13
Category : Mathematics
ISBN : 9783031427602
This book lays the foundation for a theory of coarse groups: namely, sets with operations that satisfy the group axioms “up to uniformly bounded error”. These structures are the group objects in the category of coarse spaces, and arise naturally as approximate subgroups, or as coarse kernels. The first aim is to provide a standard entry-level introduction to coarse groups. Extra care has been taken to give a detailed, self-contained and accessible account of the theory. The second aim is to quickly bring the reader to the forefront of research. This is easily accomplished, as the subject is still young, and even basic questions remain unanswered. Reflecting its dual purpose, the book is divided into two parts. The first part covers the fundamentals of coarse groups and their actions. Here the theory of coarse homomorphisms, quotients and subgroups is developed, with proofs of coarse versions of the isomorphism theorems, and it is shown how coarse actions are related to fundamental aspects of geometric group theory. The second part, which is less self-contained, is an invitation to further research, where each thread leads to open questions of varying depth and difficulty. Among other topics, it explores coarse group structures on set-groups, groups of coarse automorphisms and spaces of controlled maps. The main focus is on connections between the theory of coarse groups and classical subjects, including: number theory; the study of bi-invariant metrics on groups; quasimorphisms and stable commutator length; groups of outer automorphisms; and topological groups and their actions. The book will primarily be of interest to researchers and graduate students in geometric group theory, topology, category theory and functional analysis, but some parts will also be accessible to advanced undergraduates.
Author : Ken’ichi Ohshika
Publisher : Springer Nature
Page : 456 pages
File Size : 42,6 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9783031435027
Author : Aaron Wootton,S. Allen Broughton,Jennifer Paulhus
Publisher : American Mathematical Society
Page : 366 pages
File Size : 44,5 Mb
Release : 2022-02-03
Category : Mathematics
ISBN : 9781470460259
Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.
Author : Thomas Bloom,David W. Catlin,John P. D'Angelo,Yum-Tong Siu
Publisher : Princeton University Press
Page : 360 pages
File Size : 45,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882571
The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well-presented introduction to the most recent important developments in the field. The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster.
Author : Panos M. Pardalos,Themistocles M. Rassias
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 51,6 Mb
Release : 2012-08-07
Category : Mathematics
ISBN : 9783642288210
The volume is dedicated to Stephen Smale on the occasion of his 80th birthday.Besides his startling 1960 result of the proof of the Poincar ́e conjecture for all dimensionsgreater than or equal to five, Smale’s ground breaking contributions invarious fields in Mathematics have marked the second part of the 20th century andbeyond. Stephen Smale has done pioneering work in differential topology, globalanalysis, dynamical systems, nonlinear functional analysis, numerical analysis, theoryof computation and machine learning as well as applications in the physical andbiological sciences and economics. In sum, Stephen Smale has manifestly brokenthe barriers among the different fields of mathematics and dispelled some remainingprejudices. He is indeed a universal mathematician. Smale has been honoredwith several prizes and honorary degrees including, among others, the Fields Medal(1966), The Veblen Prize (1966), the National Medal of Science (1996) and theWolfPrize (2006/2007).
Author : Dimitrios Ntalampekos
Publisher : Springer Nature
Page : 186 pages
File Size : 55,9 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030508050
This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpiński carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces. The first part focuses on the development of an innovative theory of harmonic functions that is suitable for Sierpiński carpets but differs from the classical approach of potential theory in metric spaces. The second part describes how this theory is utilized to prove a uniformization result for Sierpiński carpets. This book is intended for researchers in the fields of potential theory, quasiconformal geometry, geometric group theory, complex dynamics, geometric function theory and PDEs.
Author : Leon Greenberg
Publisher : Princeton University Press
Page : 452 pages
File Size : 51,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881642
Study 79 contains a collection of papers presented at the Conference on Discontinuous Groups and Ricmann Surfaces at the University of Maryland, May 21-25, 1973. The papers, by leading authorities, deal mainly with Fuchsian and Kleinian groups, Teichmüller spaces, Jacobian varieties, and quasiconformal mappings. These topics are intertwined, representing a common meeting of algebra, geometry, and analysis.
Author : Sang-hyun Kim,Thomas Koberda,Mahan Mj
Publisher : Springer
Page : 136 pages
File Size : 52,5 Mb
Release : 2019-01-02
Category : Mathematics
ISBN : 9783030028558
In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.
Author : Curtis T. McMullen
Publisher : Princeton University Press
Page : 264 pages
File Size : 55,8 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865178
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
