Mappings With Direct And Inverse Poletsky Inequalities

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Mappings with Direct and Inverse Poletsky Inequalities

Author : Evgeny Sevost'yanov
Publisher : Springer Nature
ISBN 13 : 3031454189
Total Pages : 437 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Mappings with Direct and Inverse Poletsky Inequalities by : Evgeny Sevost'yanov

Download or read book Mappings with Direct and Inverse Poletsky Inequalities written by Evgeny Sevost'yanov and published by Springer Nature. This book was released on 2023-12-22 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1884 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Boletín de la Sociedad Matemática Mexicana

Author : Sociedad Matemática Mexicana
Publisher :
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Boletín de la Sociedad Matemática Mexicana by : Sociedad Matemática Mexicana

Download or read book Boletín de la Sociedad Matemática Mexicana written by Sociedad Matemática Mexicana and published by . This book was released on 2003 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Moduli in Modern Mapping Theory

Author : Olli Martio
Publisher : Springer Science & Business Media
ISBN 13 : 0387855882
Total Pages : 368 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Moduli in Modern Mapping Theory by : Olli Martio

Download or read book Moduli in Modern Mapping Theory written by Olli Martio and published by Springer Science & Business Media. This book was released on 2008-11-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

Quasiregular Mappings

Author : Seppo Rickman
Publisher : Springer Science & Business Media
ISBN 13 : 3642782019
Total Pages : 221 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Quasiregular Mappings by : Seppo Rickman

Download or read book Quasiregular Mappings written by Seppo Rickman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasiregular Mappings extend quasiconformal theory to the noninjective case.They give a natural and beautiful generalization of the geometric aspects ofthe theory of analytic functions of one complex variable to Euclidean n-space or, more generally, to Riemannian n-manifolds. This book is a self-contained exposition of the subject. A braod spectrum of results of both analytic and geometric character are presented, and the methods vary accordingly. The main tools are the variational integral method and the extremal length method, both of which are thoroughly developed here. Reshetnyak's basic theorem on discreteness and openness is used from the beginning, but the proof by means of variational integrals is postponed until near the end. Thus, the method of extremal length is being used at an early stage and leads, among other things, to geometric proofs of Picard-type theorems and a defect relation, which are some of the high points of the present book.

Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics

Author : Vesna Todorčević
Publisher : Springer
ISBN 13 : 9783030225933
Total Pages : 163 pages
Book Rating : 4.2/5 (259 download)

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Book Synopsis Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics by : Vesna Todorčević

Download or read book Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics written by Vesna Todorčević and published by Springer. This book was released on 2020-08-15 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.

Fractal Geometry and Stochastics VI

Author : Uta Freiberg
Publisher : Springer Nature
ISBN 13 : 3030596494
Total Pages : 307 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Fractal Geometry and Stochastics VI by : Uta Freiberg

Download or read book Fractal Geometry and Stochastics VI written by Uta Freiberg and published by Springer Nature. This book was released on 2021-03-23 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.

Analytic Topology

Author : Gordon Thomas Whyburn
Publisher : American Mathematical Soc.
ISBN 13 : 0821810286
Total Pages : 295 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analytic Topology by : Gordon Thomas Whyburn

Download or read book Analytic Topology written by Gordon Thomas Whyburn and published by American Mathematical Soc.. This book was released on 1963 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The material here presented represents an elaboration on my Colloquium Lectures delivered before the American Mathematical Society at its September, 1940 meeting at Dartmouth College." - Preface.

J-holomorphic Curves and Symplectic Topology

Author : Dusa McDuff
Publisher : American Mathematical Soc.
ISBN 13 : 0821887467
Total Pages : 744 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis J-holomorphic Curves and Symplectic Topology by : Dusa McDuff

Download or read book J-holomorphic Curves and Symplectic Topology written by Dusa McDuff and published by American Mathematical Soc.. This book was released on 2012 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.

The Beltrami Equation

Author : Vladimir Gutlyanskii
Publisher : Springer Science & Business Media
ISBN 13 : 1461431913
Total Pages : 309 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis The Beltrami Equation by : Vladimir Gutlyanskii

Download or read book The Beltrami Equation written by Vladimir Gutlyanskii and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Approximation, Complex Analysis, and Potential Theory

Author : Norair Arakelian
Publisher : Springer Science & Business Media
ISBN 13 : 9401009791
Total Pages : 275 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Approximation, Complex Analysis, and Potential Theory by : Norair Arakelian

Download or read book Approximation, Complex Analysis, and Potential Theory written by Norair Arakelian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here. Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures. A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.

Lectures on Analysis on Metric Spaces

Author : Juha Heinonen
Publisher : Springer Science & Business Media
ISBN 13 : 9780387951041
Total Pages : 158 pages
Book Rating : 4.9/5 (51 download)

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Book Synopsis Lectures on Analysis on Metric Spaces by : Juha Heinonen

Download or read book Lectures on Analysis on Metric Spaces written by Juha Heinonen and published by Springer Science & Business Media. This book was released on 2001 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.

Conformal Geometry and Quasiregular Mappings

Author : Matti Vuorinen
Publisher : Springer
ISBN 13 : 3540392076
Total Pages : 228 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Conformal Geometry and Quasiregular Mappings by : Matti Vuorinen

Download or read book Conformal Geometry and Quasiregular Mappings written by Matti Vuorinen and published by Springer. This book was released on 2006-11-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook and of a research monograph: it is the first introduction to the subject available in English, contains nearly a hundred exercises, a survey of the subject as well as an extensive bibliography and, finally, a list of open problems.

Sobolev Met Poincare

Author : Piotr Hajłasz
Publisher : American Mathematical Soc.
ISBN 13 : 0821820478
Total Pages : 119 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Sobolev Met Poincare by : Piotr Hajłasz

Download or read book Sobolev Met Poincare written by Piotr Hajłasz and published by American Mathematical Soc.. This book was released on 2000 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several generalizations of the classical theory of Sobolev spaces as they are necessary for the applications to Carnot-Caratheodory spaces, subelliptic equations, quasiconformal mappings on Carnot groups and more general Loewner spaces, analysis on topological manifolds, potential theory on infinite graphs, analysis on fractals and the theory of Dirichlet forms. The aim of this paper is to present a unified approach to the theory of Sobolev spaces that covers applications to many of those areas. The variety of different areas of applications forces a very general setting. We are given a metric space $X$ equipped with a doubling measure $\mu$. A generalization of a Sobolev function and its gradient is a pair $u\in L^{1}_{\rm loc}(X)$, $0\leq g\in L^{p}(X)$ such that for every ball $B\subset X$ the Poincare-type inequality $ \intbar_{B} u-u_{B} \, d\mu \leq C r ( \intbar_{\sigma B} g^{p}\, d\mu)^{1/p}\,$ holds, where $r$ is the radius of $B$ and $\sigma\geq 1$, $C>0$ are fixed constants. Working in the above setting we show that basically all relevant results from the classical theory have their counterparts in our general setting. These include Sobolev-Poincare type embeddings, Rellich-Kondrachov compact embedding theorem, and even a version of the Sobolev embedding theorem on spheres. The second part of the paper is devoted to examples and applications in the above mentioned areas.

A First Course in Complex Analysis

Author : Matthias Beck
Publisher : Orthogonal Publishing L3c
ISBN 13 : 9781944325084
Total Pages : 214 pages
Book Rating : 4.3/5 (25 download)

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Book Synopsis A First Course in Complex Analysis by : Matthias Beck

Download or read book A First Course in Complex Analysis written by Matthias Beck and published by Orthogonal Publishing L3c. This book was released on 2018-09 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Complex Analysis was developed from lecture notes for a one-semester undergraduate course taught by the authors. For many students, complex analysis is the first rigorous analysis (if not mathematics) class they take, and these notes reflect this. The authors try to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated from scratch.

Making Mathematics Come to Life

Author : Oleg A. Ivanov
Publisher : American Mathematical Soc.
ISBN 13 : 0821848089
Total Pages : 349 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Making Mathematics Come to Life by : Oleg A. Ivanov

Download or read book Making Mathematics Come to Life written by Oleg A. Ivanov and published by American Mathematical Soc.. This book was released on 2009-12-16 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: ``It is difficult to define the genre of the book. It is not a problem book, nor a textbook, nor a `book for reading about mathematics'. It is most of all reminiscent of a good lecture course, from which a thoughtful student comes away with more than was actually spoken about in the lectures.'' --from the Preface by A. S. Merkurjev If you are acquainted with mathematics at least to the extent of a standard high school curriculum and like it enough to want to learn more, and if, in addition, you are prepared to do some serious work, then you should start studying this book. An understanding of the material of the book requires neither a developed ability to reason abstractly nor skill in using the refined techniques of mathematical analysis. In each chapter elementary problems are considered, accompanied by theoretical material directly related to them. There are over 300 problems in the book, most of which are intended to be solved by the reader. In those places in the book where it is natural to introduce concepts outside the high school syllabus, the corresponding definitions are given with examples. And in order to bring out the meaning of such concepts clearly, appropriate (but not too many) theorems are proved concerning them. Unfortunately, what is sometimes studied at school under the name ``mathematics'' resembles real mathematics not any closer than a plucked flower gathering dust in a herbarium or pressed between the pages of a book resembles that same flower in the meadow besprinkled with dewdrops sparkling in the light of the rising sun.

$J$-Holomorphic Curves and Quantum Cohomology

Author : Dusa McDuff
Publisher : American Mathematical Soc.
ISBN 13 : 0821803328
Total Pages : 220 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $J$-Holomorphic Curves and Quantum Cohomology by : Dusa McDuff

Download or read book $J$-Holomorphic Curves and Quantum Cohomology written by Dusa McDuff and published by American Mathematical Soc.. This book was released on 1994 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: J -holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full account of the theory of J -holomorphic curves, the details of which are presently scattered in various research papers. The first half of the book is an expository account of the field, explaining the main technical aspects. McDuff and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that the quantum multiplication exists and is associative on appropriate manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmanians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed.