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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.

Analysis and Geometry of Metric Measure Spaces

2013 Mathematics
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Release : 2013
Genre : Mathematics
Kind : eBook
Book Rating : 188/5 ( reviews)

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Book Synopsis Analysis and Geometry of Metric Measure Spaces by : Galia Devora Dafni

Download or read book Analysis and Geometry of Metric Measure Spaces written by Galia Devora Dafni. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Trends in Analysis and Geometry

2020-01-24 Mathematics
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Release : 2020-01-24
Genre : Mathematics
Kind : eBook
Book Rating : 128/5 ( reviews)

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Book Synopsis New Trends in Analysis and Geometry by : Mohamed A. Khamsi

Download or read book New Trends in Analysis and Geometry written by Mohamed A. Khamsi. This book was released on 2020-01-24. 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.

Geometry and Analysis of Metric Spaces via Weighted Partitions

2020-11-16 Mathematics
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Release : 2020-11-16
Genre : Mathematics
Kind : eBook
Book Rating : 541/5 ( reviews)

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Book Synopsis Geometry and Analysis of Metric Spaces via Weighted Partitions by : Jun Kigami

Download or read book Geometry and Analysis of Metric Spaces via Weighted Partitions written by Jun Kigami. This book was released on 2020-11-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

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