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Author : Bernt K. Øksendal
Publisher : Unknown
Page : 40 pages
File Size : 55,5 Mb
Release : 1987
Category : Electronic
ISBN : 8255306382
Author : F. Di Biase
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461223108
A basic principle governing the boundary behaviour of holomorphic func tions (and harmonic functions) is this: Under certain growth conditions, for almost every point in the boundary of the domain, these functions ad mit a boundary limit, if we approach the bounda-ry point within certain approach regions. For example, for bounded harmonic functions in the open unit disc, the natural approach regions are nontangential triangles with one vertex in the boundary point, and entirely contained in the disc [Fat06]. In fact, these natural approach regions are optimal, in the sense that convergence will fail if we approach the boundary inside larger regions, having a higher order of contact with the boundary. The first theorem of this sort is due to J. E. Littlewood [Lit27], who proved that if we replace a nontangential region with the rotates of any fixed tangential curve, then convergence fails. In 1984, A. Nagel and E. M. Stein proved that in Euclidean half spaces (and the unit disc) there are in effect regions of convergence that are not nontangential: These larger approach regions contain tangential sequences (as opposed to tangential curves). The phenomenon discovered by Nagel and Stein indicates that the boundary behaviour of ho)omor phic functions (and harmonic functions), in theorems of Fatou type, is regulated by a second principle, which predicts the existence of regions of convergence that are sequentially larger than the natural ones.
Author : Mark A. Pinsky,AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Geometry of Random Motion
Publisher : American Mathematical Soc.
Page : 337 pages
File Size : 52,9 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850817
In July 1987, an AMS-IMS-SIAM Joint Summer Research Conference on Geometry of Random Motion was held at Cornell University. The initial impetus for the meeting came from the desire to further explore the now-classical connection between diffusion processes and second-order (hypo)elliptic differential operators. To accomplish this goal, the conference brought together leading researchers with varied backgrounds and interests: probabilists who have proved results in geometry, geometers who have used probabilistic methods, and probabilists who have studied diffusion processes. Focusing on the interplay between probability and differential geometry, this volume examines diffusion processes on various geometric structures, such as Riemannian manifolds, Lie groups, and symmetric spaces. Some of the articles specifically address analysis on manifolds, while others center on (nongeometric) stochastic analysis. The majority of the articles deal simultaneously with probabilistic and geometric techniques. Requiring a knowledge of the modern theory of diffusion processes, this book will appeal to mathematicians, mathematical physicists, and other researchers interested in Brownian motion, diffusion processes, Laplace-Beltrami operators, and the geometric applications of these concepts. The book provides a detailed view of the leading edge of research in this rapidly moving field.
Author : Matti Vuorinen
Publisher : Springer
Page : 156 pages
File Size : 52,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470618
This volume is a collection of surveys on function theory in euclidean n-dimensional spaces centered around the theme of quasiconformal space mappings. These surveys cover or are related to several topics including inequalities for conformal invariants and extremal length, distortion theorems, L(p)-theory of quasiconformal maps, nonlinear potential theory, variational calculus, value distribution theory of quasiregular maps, topological properties of discrete open mappings, the action of quasiconformal maps in special classes of domains, and global injectivity theorems. The present volume is the first collection of surveys on Quasiconformal Space Mappings since the origin of the theory in 1960 and this collection provides in compact form access to a wide spectrum of recent results due to well-known specialists. CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen: Conformal invariants, quasiconformal maps and special functions.- F.W. Gehring: Topics in quasiconformal mappings.- T.Iwaniec: L(p)-theory of quasiregular mappings.- O. Martio: Partial differential equations and quasiregular mappings.- Yu.G. Reshetnyak: On functional classes invariant relative to homothetics.- S. Rickman: Picard's theorem and defect relation for quasiconformal mappings.- U. Srebro: Topological properties of quasiregular mappings.- J. V{is{l{: Domains and maps.- V.A. Zorich: The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems.
Author : Seppo Rickman
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642782015
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.
Author : Juha Heinonen,Tero Kipelainen,Olli Martio
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 42,9 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486824253
A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.
Author : Matti Vuorinen
Publisher : Springer
Page : 228 pages
File Size : 41,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540392071
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.
Author : Anonim
Publisher : Unknown
Page : 618 pages
File Size : 41,7 Mb
Release : 1967
Category : American periodicals
ISBN : UCAL:B4483119
Author : Tadeusz Iwaniec,Gaven Martin
Publisher : Clarendon Press
Page : 576 pages
File Size : 50,8 Mb
Release : 2001
Category : Language Arts & Disciplines
ISBN : 0198509294
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 : Treven Parker Wall
Publisher : Unknown
Page : 106 pages
File Size : 42,7 Mb
Release : 2007
Category : Electronic
ISBN : CORNELL:31924107954178
Author : Fausto Di Biase
Publisher : Unknown
Page : 152 pages
File Size : 55,6 Mb
Release : 1997
Category : Fatou theorems
ISBN : OCLC:637730917
Author : B. Dahlberg,Eugene Fabes,R. Fefferman,David Jerison,Carlos Kenig,J. Pipher
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461228981
In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.
Author : Suomalainen Tiedeakatemia
Publisher : Unknown
Page : 612 pages
File Size : 44,7 Mb
Release : 1983
Category : Mathematics
ISBN : UCSD:31822020303723
Author : Jyväskylän yliopisto. Matematiikan laitos
Publisher : Unknown
Page : 358 pages
File Size : 52,6 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015048176070
Author : Nessim Sibony,Dierk Schleicher,Dinh Tien Cuong,Marco Brunella,Eric Bedford,Marco Abate
Publisher : Springer
Page : 348 pages
File Size : 41,8 Mb
Release : 2010-07-20
Category : Mathematics
ISBN : 9783642131714
The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.