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Lectures on Analysis on Metric Spaces

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 319/5 ( reviews)

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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. This book was released on 2012-12-06. 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.

Introduction to the Analysis of Metric Spaces

1987-09-03 Mathematics
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Release : 1987-09-03
Genre : Mathematics
Kind : eBook
Book Rating : 283/5 ( reviews)

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Book Synopsis Introduction to the Analysis of Metric Spaces by : John R. Giles

Download or read book Introduction to the Analysis of Metric Spaces written by John R. Giles. This book was released on 1987-09-03. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on analysis in metric spaces

2001-10-01 Mathematics
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Release : 2001-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 553/5 ( reviews)

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Book Synopsis Lectures on analysis in metric spaces by : Luigi Ambrosio

Download or read book Lectures on analysis in metric spaces written by Luigi Ambrosio. This book was released on 2001-10-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Trends on Analysis and Geometry in Metric Spaces

2022-02-04 Mathematics
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Release : 2022-02-04
Genre : Mathematics
Kind : eBook
Book Rating : 413/5 ( reviews)

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Book Synopsis New Trends on Analysis and Geometry in Metric Spaces by : Fabrice Baudoin

Download or read book New Trends on Analysis and Geometry in Metric Spaces written by Fabrice Baudoin. This book was released on 2022-02-04. 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.

Gradient Flows

2008-10-29 Mathematics
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Release : 2008-10-29
Genre : Mathematics
Kind : eBook
Book Rating : 22X/5 ( reviews)

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Book Synopsis Gradient Flows by : Luigi Ambrosio

Download or read book Gradient Flows written by Luigi Ambrosio. This book was released on 2008-10-29. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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