This book is a polished version of Heinonen's notes from a class he taught at Michigan.

This book is a polished version of Heinonen's notes from a class he taught at Michigan. That means it offers a brief, broad sweep of the field, picking out some highlights and helping a newcomer orient themself without attempting to be comprehensive. The closest would be "Topics in Analysis on Metric Spaces" by Ambrosio and Tilli, which covers similar material but more from the vantage point of geometric measure theory (whereas Heinonen's book comes from the tradition of quasiconformal mappings). Perhaps one would also consider "A Course in Metric Geometry" by Burago, Burago, and Ivanov, though their focus is on Alexandrov geometry.

The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces.

In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general settings; abstract Sobolev space theories have been instrumental in this development. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is relatively recent and appears for the first time in book format. There are plenty of exercises. The book is well suited for self-study, or as a text in a graduate course or seminar.

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Автор: Heinonen Juha Название: Lectures on Analysis on Metric Spaces Издательство: Springer Классификация .

Lectures on Analysis on Metric Spaces.

Such studies have applications to geometric rigidity questions, but are also of intrinsic interest. Lectures on Analysis on Metric Spaces.

Start by marking Lectures on Analysis on Metric Spaces as Want to Read . The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study.

Start by marking Lectures on Analysis on Metric Spaces as Want to Read: Want to Read savin. ant to Read. 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.

Book information: Year: 2001. Author: Juha Heinonen. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts.

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