The Beltrami Equation: A Geometric Approach: 26 (Developments in Mathematics) - Hardcover
Buch 23 von 67: Developments in Mathematics
Inhaltsangabe
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.
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The Beltrami Equation: A Geometric Approach will be particularly useful to many specialists in modern geometric analysis, quasiconformal mappings and extensions, beginning researchers, and graduate students with a year s background in complex variables. This book covers the state-of-the art in the ongoing study of the Beltrami equation, the classical equation that has been studied for more than 100 years. Along with its rich history, the Beltrami equation plays a significant role in geometry, analysis, and physics.
The most important feature of this work concerns the unified geometric approach taken based on the modulus method that can be effectively applied to solving many problems in mathematical physics. Beautiful examples illustrate the relationship between mappings with bounded oscillation and those with finite oscillations.
Written by authors that are well-known specialists in this field, this monograph presents recent developments in the theory of Beltrami equations, studying a variety of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates, and boundary behavior of solutions to the Beltrami equations. It contains 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.
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The Beltrami Equation: A Geometric Approach (Developments in Mathematics, Vol. 26)
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Hardcover. Zustand: Very Good. 1st Edition. Hardcover, xiii + 301 pages, NOT ex-library. Clean and bright throughout. Some internal creasing. Issued without a dust jacket. - A treatment of Beltrami equations, with a focus on a unified geometric approach based on the modulus method. This monograph serves both as a reference work and pedagogical text for graduate-level readers engaged in research on quasiconformal mappings, complex analysis, and nonlinear elliptic partial differential equations. It is especially relevant for contemporary mathematical investigations involving generalized and degenerate structures, boundary value problems, and geometric analysis. At the heart of the book is the Beltrami equation "f sub z-bar equals mu of z times f sub z", a fundamental nonlinear PDE that generalizes the Cauchy-Riemann equations. This equation plays a central role in the theory of quasiconformal mappings, which in turn are deeply connected to Teichmüller theory, Riemann surfaces, low-dimensional topology, and various areas in mathematical physics. The authors present a geometric method founded on modulus and capacity theory, allowing for new insights into problems such as existence, uniqueness, convergence, distortion, and boundary behavior of solutions under general, degenerate, or singular conditions. The book is structured into ten chapters that progressively develop the analytic and geometric theory of Beltrami equations. After an introductory chapter that contextualizes the equation within geometry, analysis, and applications, the authors establish foundational material in Chapter 2, covering BMO and FMO function spaces, Sobolev classes, modulus, capacity, convergence theorems, and integral conditions. These preliminaries support later rigorous treatments of classical and degenerate Beltrami equations. Chapters 3 & 4 examine the classical equation "essential supremum of the absolute value of mu is strictly less than one" and its degenerate forms. The degenerate case, which includes singularities and sets where "the absolute value of mu is equal to one" is especially relevant for modern research, as it captures behaviors arising in limiting configurations and critical geometric flows. Through new integral conditions, the authors unify and extend many existing results, establishing criteria that are both necessary and sufficient for solvability in degenerate domains. Chapters 5 & 6 study BMO- and FMO-quasiconformal mappings and ring Q-homeomorphisms at boundary points. The development of distortion estimates, existence theorems, and removability results reflects a significant methodological advancement, particularly the refinement of local and boundary regularity conditions. These tools are essential in modern complex dynamics and potential theory, especially in settings where traditional smoothness assumptions are too restrictive. Chapter 7 introduces the notion of strong ring solutions, including factorization techniques and integral characterizations that allow for a robust treatment of Beltrami equations with measurable coefficients. This facilitates deeper engagement with the non-linear and non-uniform elliptic structures present in various applied contexts. Chapter 8 addresses the Dirichlet problem under generalized Beltrami conditions. This discussion includes new integral criteria for existence, regularity of homeomorphic solutions, and techniques for extending mappings to the boundary - a topic of importance in the study of Riemann surfaces and variational methods. Chapters 9 & 10 explore more recent developments: Beltrami equations with two characteristics and alternating Beltrami equations. These extensions are crucial in studying branched and folded mappings, which have applications in image processing, geometric function theory, and the modeling of material deformations. The detailed classifications and constructions of BF-maps (branched folded maps) and cusp structures provide a novel toolkit for researchers analyzing discontinuous or multi-valued phenomena. Bestandsnummer des Verkäufers 011373
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 316 pp. Englisch. Bestandsnummer des Verkäufers 9781461431909
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The Beltrami Equation | A Geometric Approach
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Buch. Zustand: Neu. The Beltrami Equation | A Geometric Approach | Vladimir Gutlyanskii (u. a.) | Buch | xiv | Englisch | 2012 | Springer US | EAN 9781461431909 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Bestandsnummer des Verkäufers 106678256
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Buch. Zustand: Neu. Neuware -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; especiallythose 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 behaviorof solutions to the Beltrami equations. The monographcontains 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 bookconcerns 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 alsogives 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.¿Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 316 pp. Englisch. Bestandsnummer des Verkäufers 9781461431909
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ISBN 10: 1461431905
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Bestandsnummer des Verkäufers 9781461431909
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