[PDF] Geometric Function Theory eBook

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 40,48 MB
Release : 2001
Category : Mathematics
ISBN : 0821827243

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Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 43,23 MB
Release : 2007-09-19
Category : Mathematics
ISBN : 0817644407

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* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

Author : Ian Graham
Publisher : CRC Press
Page : 572 pages
File Size : 20,85 MB
Release : 2003-03-18
Category : Mathematics
ISBN : 9780203911624

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This reference details valuable results that lead to improvements in existence theorems for the Loewner differential equation in higher dimensions, discusses the compactness of the analog of the Caratheodory class in several variables, and studies various classes of univalent mappings according to their geometrical definitions. It introduces the in

Author : Tadeusz Iwaniec
Publisher : Clarendon Press
Page : 576 pages
File Size : 35,23 MB
Release : 2001
Category : Language Arts & Disciplines
ISBN : 9780198509295

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Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.

Author : Junjirō Noguchi
Publisher : American Mathematical Soc.
Page : 292 pages
File Size : 16,96 MB
Release : 1990
Category : Mathematics
ISBN : 9780821845332

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An English translation of a book that first appeared in Japanese. It provides an account of recent developments in geometric function theory in several complex variables and presents fundamental descriptions of positive currents, plurisubharmonic functions and meromorphic mappings.

Author : Reiner Kuhnau
Publisher : Elsevier
Page : 549 pages
File Size : 24,4 MB
Release : 2002-12-05
Category : Mathematics
ISBN : 0080532810

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Geometric 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 : M. Grosser
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 39,7 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 9401598452

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Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.

Author : Filippo Bracci
Publisher : Springer
Page : 185 pages
File Size : 24,69 MB
Release : 2018-03-24
Category : Mathematics
ISBN : 3319731262

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The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.

Author : Vladimir N. Dubinin
Publisher : Springer
Page : 352 pages
File Size : 48,71 MB
Release : 2014-08-20
Category : Science
ISBN : 3034808437

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This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original – the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problems are solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven. This book will be a valuable source for current and future researchers in various branches of complex analysis and potential theory.