New Trends On Analysis And Geometry In Metric Spaces

Author : Fabrice Baudoin
Publisher : Springer Nature
ISBN 13 : 3030841413
Total Pages : 312 pages
Book Rating : 4.16/5 ( download)

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Download or read book New Trends on Analysis and Geometry in Metric Spaces written by Fabrice Baudoin and published by Springer Nature. This book was released on 2022-02-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Juha Heinonen
Publisher : Springer Science & Business Media
ISBN 13 : 1461301319
Total Pages : 149 pages
Book Rating : 4.18/5 ( download)

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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 2012-12-06 with total page 149 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.

Author : Mohamed A. Khamsi
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1527546128
Total Pages : 401 pages
Book Rating : 4.27/5 ( download)

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Download or read book New Trends in Analysis and Geometry written by Mohamed A. Khamsi and published by Cambridge Scholars Publishing. This book was released on 2020-01-24 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Cambridge University Press
ISBN 13 : 1107092345
Total Pages : 447 pages
Book Rating : 4.41/5 ( download)

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Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Author : Dorina Mitrea
Publisher : Springer Science & Business Media
ISBN 13 : 0817683976
Total Pages : 486 pages
Book Rating : 4.79/5 ( download)

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Download or read book Groupoid Metrization Theory written by Dorina Mitrea and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Antonio Alarcón
Publisher : Springer Nature
ISBN 13 : 3031399161
Total Pages : 398 pages
Book Rating : 4.69/5 ( download)

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Download or read book New Trends in Geometric Analysis written by Antonio Alarcón and published by Springer Nature. This book was released on 2023-11-25 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Piotr W. Nowak
Publisher : European Mathematical Society
ISBN 13 : 3985470189
Total Pages : 0 pages
Book Rating : 4.81/5 ( download)

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Download or read book Large Scale Geometry written by Piotr W. Nowak and published by European Mathematical Society. This book was released on 2023-07-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large scale geometry is the study of geometric objects viewed from a great distance. The idea of large scale geometry can be traced back to Mostow's work on rigidity and the work of Švarc, Milnor, and Wolf on growth of groups and is greatly influenced by Gromov's work on geometric group theory. In the last decades, large scale geometry has found important applications in group theory, topology, geometry, higher index theory, computer science, and large data analysis. This book provides a friendly approach to the basic theory of this exciting and fast growing subject and offers a glimpse of its applications to topology, geometry, and higher index theory. The authors have made a conscientious effort to make the book accessible to advanced undergraduate students, graduate students, and non-experts. The second edition has been updated to cover recent developments involving constructions of groups and metric spaces with exotic properties as well as results charting new directions in index theory, and it also includes minor improvements in the presentation and an updated bibliography.

Author : Satish Shirali
Publisher : Springer Science & Business Media
ISBN 13 : 1846282446
Total Pages : 230 pages
Book Rating : 4.47/5 ( download)

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Download or read book Metric Spaces written by Satish Shirali and published by Springer Science & Business Media. This book was released on 2005-12-16 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily

Author : Amar Kumar Banerjee
Publisher :
ISBN 13 : 9781906574956
Total Pages : 0 pages
Book Rating : 4.52/5 ( download)

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Download or read book Metric Spaces and Complex Analysis written by Amar Kumar Banerjee and published by . This book was released on 2013-05-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book Metric Spaces and Complex Analysis, is to provide a preliminary but comprehensive knowledge of metric spaces as well as complex analysis to the beginners. However, this work is expected to serve well as an aid to advanced graduate students studying these topics because the topological ideas dealt with here can be enjoyed with an elementary knowledge of real analysis and geometry. For clarity of visualisation, pictorial representation of main items has been given a priority, wherever necessary. The volume is enriched with numerous illustrations so as to make it user-friendly. It contains approximately fifty diagrams, and more than hundred examples and nearly one hundred fifty exercises

Author : Victor Bryant
Publisher : Cambridge University Press
ISBN 13 : 9780521268578
Total Pages : 112 pages
Book Rating : 4.75/5 ( download)

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Download or read book Metric Spaces written by Victor Bryant and published by Cambridge University Press. This book was released on 1985-05-02 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis.