New Trends On Analysis And Geometry In Metric Spaces

Author : Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam
Publisher : Springer Nature
Page : 312 pages
File Size : 53,5 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 : Mohamed A. Khamsi
Publisher : Cambridge Scholars Publishing
Page : 401 pages
File Size : 44,8 Mb
Release : 2020-01-24
Category : Mathematics
ISBN : 9781527546127

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New Trends in Analysis and Geometry by Mohamed A. Khamsi Pdf

This unique mathematical volume brings together geometers, analysts, differential equations specialists and graph-theorists to provide a glimpse on recent mathematical trends whose commonalities have hitherto remained, for the most part, unnoticed. The applied mathematician will be pleasantly surprised with the interpretation of a voting system in terms of the fixed points of a mapping given in the book, as much as the classical analyst will be enthusiastic to find detailed discussions on the generalization of the notion of metric space, in which the metric takes values on an abstract monoid. Classical themes on fixed point theory are adapted to the diverse setting of graph theory, thus uncovering a set of tools whose power and versatility will be appreciated by mathematicians working on either area. The volume also includes recent results on variable exponent spaces which reveal much-needed connections with partial differential equations, while the incipient field of variational inequalities on manifolds, also explored here, will be of interest to researchers from a variety of fields.

Author : Juha Heinonen
Publisher : Springer Science & Business Media
Page : 149 pages
File Size : 45,9 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 : Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson
Publisher : Cambridge University Press
Page : 447 pages
File Size : 55,6 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 : Amar Kumar Banerjee
Publisher : New Age International
Page : 27 pages
File Size : 45,9 Mb
Release : 2008
Category : Electronic
ISBN : 9788122422603

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Metric Spaces and Complex Analysis by Amar Kumar Banerjee Pdf

Author : Luigi Ambrosio,Paolo Tilli
Publisher : Oxford University Press on Demand
Page : 18 pages
File Size : 40,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780198529385

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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 : Dorina Mitrea,Irina Mitrea,Marius Mitrea,Sylvie Monniaux
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 55,9 Mb
Release : 2012-12-15
Category : Mathematics
ISBN : 9780817683979

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Groupoid Metrization Theory by Dorina Mitrea,Irina Mitrea,Marius Mitrea,Sylvie Monniaux Pdf

The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis include: * treatment of metrization from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields; * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties.

Author : Alexander Brudnyi,Prof. Yuri Brudnyi Technion R&D Foundation Ltd
Publisher : Birkhäuser
Page : 564 pages
File Size : 48,8 Mb
Release : 2013-11-30
Category : Mathematics
ISBN : 3034803389

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Methods of Geometric Analysis in Extension and Trace Problems by Alexander Brudnyi,Prof. Yuri Brudnyi Technion R&D Foundation Ltd Pdf

The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.

Author : Victor Bryant
Publisher : Cambridge University Press
Page : 116 pages
File Size : 48,9 Mb
Release : 1985-05-02
Category : Mathematics
ISBN : 0521318971

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Metric Spaces by Victor Bryant Pdf

An introduction to metric spaces for those interested in the applications as well as theory.

Author : Antonio Alarcón,Vicente Palmer,César Rosales
Publisher : Springer Nature
Page : 398 pages
File Size : 45,7 Mb
Release : 2023-11-25
Category : Mathematics
ISBN : 9783031399169

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New Trends in Geometric Analysis by Antonio Alarcón,Vicente Palmer,César Rosales Pdf

The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes. On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of them authored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG. Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.

Author : Clifford Taubes
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 51,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821803233

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Metrics, Connections and Gluing Theorems by Clifford Taubes Pdf

In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but is is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.

Author : Dmitri Burago,Yuri Burago,Sergei Ivanov
Publisher : American Mathematical Society
Page : 415 pages
File Size : 43,6 Mb
Release : 2022-01-27
Category : Mathematics
ISBN : 9781470468538

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A Course in Metric Geometry by Dmitri Burago,Yuri Burago,Sergei Ivanov Pdf

“Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.

Author : Robert Magnus
Publisher : Springer Nature
Page : 258 pages
File Size : 53,5 Mb
Release : 2022-03-16
Category : Mathematics
ISBN : 9783030949464

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Metric Spaces by Robert Magnus Pdf

This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at a pace appropriate to the material. The book covers the main topics of metric space theory that the student of analysis is likely to need. Starting with an overview defining the principal examples of metric spaces in analysis (chapter 1), it turns to the basic theory (chapter 2) covering open and closed sets, convergence, completeness and continuity (including a treatment of continuous linear mappings). There is also a brief dive into general topology, showing how metric spaces fit into a wider theory. The following chapter is devoted to proving the completeness of the classical spaces. The text then embarks on a study of spaces with important special properties. Compact spaces, separable spaces, complete spaces and connected spaces each have a chapter devoted to them. A particular feature of the book is the occasional excursion into analysis. Examples include the Mazur–Ulam theorem, Picard’s theorem on existence of solutions to ordinary differential equations, and space filling curves. This text will be useful to all undergraduate students of mathematics, especially those who require metric space concepts for topics such as multivariate analysis, differential equations, complex analysis, functional analysis, and topology. It includes a large number of exercises, varying from routine to challenging. The prerequisites are a first course in real analysis of one real variable, an acquaintance with set theory, and some experience with rigorous proofs.

Author : Anton Petrunin
Publisher : Springer Nature
Page : 107 pages
File Size : 46,5 Mb
Release : 2023-12-23
Category : Mathematics
ISBN : 9783031391620

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Pure Metric Geometry by Anton Petrunin Pdf

This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport. Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in need of an introduction to metric geometry. Any previous knowledge of classical geometry, differential geometry, topology, and real analysis will be useful in understanding the presented topics.

Author : E. T. Copson
Publisher : CUP Archive
Page : 156 pages
File Size : 49,7 Mb
Release : 1988-02-11
Category : Mathematics
ISBN : 0521357322

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Metric Spaces by E. T. Copson Pdf

Professor Copson's book provides a more leisurely treatment of metric spaces than is found in books on functional analysis.