The Beltrami Equation

Author : Vladimir Gutlyanskii,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 55,9 Mb
Release : 2012-04-23
Category : Mathematics
ISBN : 9781461431916

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The Beltrami Equation by Vladimir Gutlyanskii,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov Pdf

This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.​

Author : Tadeusz Iwaniec,Gaven Martin
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 50,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780821840450

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The Beltrami Equation by Tadeusz Iwaniec,Gaven Martin Pdf

The ""measurable Riemann Mapping Theorem"" (or the existence theorem for quasiconformal mappings) has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. Anticipating the needs of future researchers, the authors give an account of the ""state of the art"" as it pertains to this theorem, that is, to the existence and uniqueness theory of the planar Beltrami equation, and various properties of the solutions to this equation. The classical theory concerns itself with the uniformly elliptic case (quasiconformal mappings). Here the authors develop the theory in the more general framework of mappings of finite distortion and the associated degenerate elliptic equations.

Author : Anonim
Publisher : Unknown
Page : 336 pages
File Size : 49,6 Mb
Release : 2004
Category : Mathematics
ISBN : UCSD:31822033898388

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Memoirs of the American Mathematical Society by Anonim Pdf

Author : Tadeusz Iwaniec,Gaven Martin
Publisher : Clarendon Press
Page : 576 pages
File Size : 44,8 Mb
Release : 2001
Category : Language Arts & Disciplines
ISBN : 0198509294

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Geometric Function Theory and Non-linear Analysis by Tadeusz Iwaniec,Gaven Martin Pdf

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 : Kari Astala,Tadeusz Iwaniec,Gaven Martin
Publisher : Princeton University Press
Page : 708 pages
File Size : 42,6 Mb
Release : 2009-01-18
Category : Mathematics
ISBN : 0691137773

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Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) by Kari Astala,Tadeusz Iwaniec,Gaven Martin Pdf

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Author : Heinrich G W Begehr
Publisher : World Scientific Publishing Company
Page : 284 pages
File Size : 48,9 Mb
Release : 1994-11-15
Category : Mathematics
ISBN : 9789813104686

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Complex Analytic Methods for Partial Differential Equations by Heinrich G W Begehr Pdf

This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincaré problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.

Author : Reiner Kuhnau
Publisher : Elsevier
Page : 876 pages
File Size : 48,9 Mb
Release : 2004-12-09
Category : Mathematics
ISBN : 9780080495170

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Handbook of Complex Analysis by Reiner Kuhnau Pdf

Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · 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 : Chung-Chun Yang,Sheng Gong
Publisher : American Mathematical Soc.
Page : 173 pages
File Size : 53,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851647

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Several Complex Variables in China by Chung-Chun Yang,Sheng Gong Pdf

Today, there is increasing interest in complex geometry, geometric function theory, and integral representation theory of several complex variables. The present collection of survey and research articles comprises a current overview of research in several complex variables in China. Among the topics covered are singular integrals, function spaces, differential operators, and factorization of meromorphic functions in several complex variables via analytic or geometric methods. Some results are reported in English for the first time.

Author : Mark Lʹvovich Agranovskiĭ,Matania Ben-Artzi,Greg Galloway,Lavi Karp,Vladimir Maz'Ya
Publisher : American Mathematical Soc.
Page : 337 pages
File Size : 54,7 Mb
Release : 2013-06-03
Category : Mathematics
ISBN : 9780821890240

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Complex Analysis and Dynamical Systems V by Mark Lʹvovich Agranovskiĭ,Matania Ben-Artzi,Greg Galloway,Lavi Karp,Vladimir Maz'Ya Pdf

This volume contains the proceedings of the Fifth International Conference on Complex Analysis and Dynamical Systems, held from May 22-27, 2011, in Akko (Acre), Israel. The papers cover a wide variety of topics in complex analysis and partial differential

Author : Edward Beltrami
Publisher : Academic Press
Page : 294 pages
File Size : 55,6 Mb
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 9781483267869

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Mathematics for Dynamic Modeling by Edward Beltrami Pdf

Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.

Author : Antonio Alarcón,Franc Forstnerič,Francisco J. López
Publisher : Springer Nature
Page : 430 pages
File Size : 48,7 Mb
Release : 2021-03-10
Category : Mathematics
ISBN : 9783030690564

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Minimal Surfaces from a Complex Analytic Viewpoint by Antonio Alarcón,Franc Forstnerič,Francisco J. López Pdf

This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 876 pages
File Size : 47,8 Mb
Release : 2007
Category : Teichm uller spaces
ISBN : 3037191031

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.

Author : Kari Astala,Tadeusz Iwaniec,Gaven Martin
Publisher : Princeton University Press
Page : 696 pages
File Size : 45,7 Mb
Release : 2008-12-29
Category : Mathematics
ISBN : 1400830117

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Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) by Kari Astala,Tadeusz Iwaniec,Gaven Martin Pdf

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Author : Léa Blanc-Centi
Publisher : Springer
Page : 173 pages
File Size : 54,5 Mb
Release : 2017-11-03
Category : Mathematics
ISBN : 9783319658377

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Metrical and Dynamical Aspects in Complex Analysis by Léa Blanc-Centi Pdf

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.

Author : I͡U. S. Ilʹi͡ashenko,S. Yakovenko
Publisher : American Mathematical Soc.
Page : 656 pages
File Size : 50,6 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821872486

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Lectures on Analytic Differential Equations by I͡U. S. Ilʹi͡ashenko,S. Yakovenko Pdf

Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text." "The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area."--BOOK JACKET.