Applications of Geometric Measure Theory to Complex and Quasiconformal Analysis
Author: Tyler Charles Bongers
Publisher:
Published: 2018
Total Pages: 98
ISBN-13: 9780355839104
DOWNLOAD EBOOKRead and Download eBook Full
Author: Tyler Charles Bongers
Publisher:
Published: 2018
Total Pages: 98
ISBN-13: 9780355839104
DOWNLOAD EBOOKAuthor: Reiner Kuhnau
Publisher: Elsevier
Published: 2002-12-05
Total Pages: 549
ISBN-13: 0080532810
DOWNLOAD EBOOKGeometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers. · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane)
Author: Leon Simon
Publisher:
Published: 2014
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: J.M. Belley
Publisher:
Published: 2014-09-01
Total Pages: 340
ISBN-13: 9783662194263
DOWNLOAD EBOOKAuthor: Frederick W. Gehring
Publisher: American Mathematical Soc.
Published: 2017-05-03
Total Pages: 442
ISBN-13: 0821843605
DOWNLOAD EBOOKThis book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background. This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.
Author: Roger Overy (Eric)
Publisher:
Published: 1973
Total Pages: 188
ISBN-13:
DOWNLOAD EBOOKAuthor: E. Bombieri
Publisher:
Published: 2011-03-30
Total Pages: 242
ISBN-13: 9783642109713
DOWNLOAD EBOOKAuthor: E. Pap
Publisher: Elsevier
Published: 2002-10-31
Total Pages: 1633
ISBN-13: 0080533094
DOWNLOAD EBOOKThe main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others. The Handbook is a rich source of relevant references to articles, books and lecture notes and it contains for the reader's convenience an extensive subject and author index.
Author: Donald L. Cohn
Publisher: Springer Science & Business Media
Published: 1994
Total Pages: 389
ISBN-13: 0817630031
DOWNLOAD EBOOKIntended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. Measure Theory provides a solid background for study in both harmonic analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are courses in topology and analysis.
Author: John M. Mackay
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 162
ISBN-13: 0821852299
DOWNLOAD EBOOKConformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.