Lectures On Analysis On Metric Spaces

Author : Juha Heinonen
Publisher : Springer Science & Business Media
Page : 149 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301318

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Lectures on Analysis on Metric Spaces by Juha Heinonen Pdf

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.

Author : John R. Giles
Publisher : Cambridge University Press
Page : 276 pages
File Size : 55,8 Mb
Release : 1987-09-03
Category : Mathematics
ISBN : 0521359287

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Introduction to the Analysis of Metric Spaces by John R. Giles Pdf

This is an introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. Assuming a basic knowledge of real analysis and linear algebra, the student is exposed to the axiomatic method in analysis and is shown its power in exploiting the structure of fundamental analysis, which underlies a variety of applications. An example is the link between normed linear spaces and linear algebra; finite dimensional spaces are discussed early. The treatment progresses from the concrete to the abstract: thus metric spaces are studied in some detail before general topology is begun, though topological properties of metric spaces are explored in the book. Graded exercises are provided at the end of each section; in each set the earlier exercises are designed to assist in the detection of the structural properties in concrete examples while the later ones are more conceptually sophisticated.

Author : Luigi Ambrosio,Francesco Serra Cassano
Publisher : Edizioni della Normale
Page : 0 pages
File Size : 41,7 Mb
Release : 2001-10-01
Category : Mathematics
ISBN : 8876422552

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Lectures on analysis in metric spaces by Luigi Ambrosio,Francesco Serra Cassano Pdf

This book contains the notes of an international summer school on Analysis in Metric Spaces. The contributions are the following: T. Coulhon, Random walks and geometry on infinite graphs; G. David, Uniform rectifiability and quasiminimal sets; P. Koskela, Upper gradients and Poincaré inequalities; S. Semmes, Derivatives and difference quotients for Lipschitz or Sobolev functions on various spaces; R. L. Wheeden, Some weighted Poincaré estimates in spaces of homogenous type.

Author : Galia Devora Dafni,Robert John McCann,Alina Stancu
Publisher : American Mathematical Soc.
Page : 241 pages
File Size : 55,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821894187

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Analysis and Geometry of Metric Measure Spaces by Galia Devora Dafni,Robert John McCann,Alina Stancu Pdf

Contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.

Author : Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam
Publisher : Springer Nature
Page : 312 pages
File Size : 49,7 Mb
Release : 2022-02-04
Category : Mathematics
ISBN : 9783030841416

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New Trends on Analysis and Geometry in Metric Spaces by Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam Pdf

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.

Author : Luigi Ambrosio,Paolo Tilli
Publisher : Oxford University Press, USA
Page : 148 pages
File Size : 51,5 Mb
Release : 2004
Category : Mathematics
ISBN : 0198529384

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Topics on Analysis in Metric Spaces by Luigi Ambrosio,Paolo Tilli Pdf

This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorums, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed on general metric spaces and as an application of the Gromov-Hausdorff theory, even in some cases when the ambient space is not locally compact. A brief and very general description of the theory of integration with respect to non-decreasing set functions is presented following the Di Giorgi method of using the 'cavalieri' formula as the definition of the integral. Based on lecture notes from Scuola Normale, this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.

Author : Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson
Publisher : Cambridge University Press
Page : 447 pages
File Size : 43,8 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9781107092341

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Sobolev Spaces on Metric Measure Spaces by Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson Pdf

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Author : Jun Kigami
Publisher : Springer
Page : 164 pages
File Size : 47,8 Mb
Release : 2020-11-17
Category : Mathematics
ISBN : 3030541533

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Geometry and Analysis of Metric Spaces via Weighted Partitions by Jun Kigami Pdf

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.

Author : Luigi Ambrosio,Nicola Gigli,Giuseppe Savare
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 41,9 Mb
Release : 2008-10-29
Category : Mathematics
ISBN : 9783764387228

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Gradient Flows by Luigi Ambrosio,Nicola Gigli,Giuseppe Savare Pdf

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Author : Juha Heinonen
Publisher : Unknown
Page : 77 pages
File Size : 46,8 Mb
Release : 2005
Category : Function spaces
ISBN : 9513923185

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Lectures on Lipschitz Analysis by Juha Heinonen Pdf

Author : Finnur Lárusson
Publisher : Cambridge University Press
Page : 128 pages
File Size : 55,9 Mb
Release : 2012-06-07
Category : Mathematics
ISBN : 9781139511049

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Lectures on Real Analysis by Finnur Lárusson Pdf

This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.

Author : S. Kumaresan
Publisher : Alpha Science Int'l Ltd.
Page : 172 pages
File Size : 55,8 Mb
Release : 2005
Category : Computers
ISBN : 1842652508

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Topology of Metric Spaces by S. Kumaresan Pdf

"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.

Author : Finnur Lárusson,Professor Finnur L Russon
Publisher : Unknown
Page : 130 pages
File Size : 49,8 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1139519034

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Lectures on Real Analysis by Finnur Lárusson,Professor Finnur L Russon Pdf

A rigorous introduction to real analysis for undergraduates. Concise yet comprehensive, it includes a gentle introduction to metric spaces.

Author : Alexander Isaev
Publisher : Springer
Page : 194 pages
File Size : 48,6 Mb
Release : 2017-11-29
Category : Mathematics
ISBN : 9783319681702

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Twenty-One Lectures on Complex Analysis by Alexander Isaev Pdf

At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.

Author : Jun Kigami
Publisher : Springer Nature
Page : 164 pages
File Size : 46,7 Mb
Release : 2020-11-16
Category : Mathematics
ISBN : 9783030541545

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Geometry and Analysis of Metric Spaces via Weighted Partitions by Jun Kigami Pdf

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.