Lectures on Analysis on Metric Spaces

  • Juha Heinonen

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Juha Heinonen
    Pages 1-9
  3. Juha Heinonen
    Pages 10-13
  4. Juha Heinonen
    Pages 14-26
  5. Juha Heinonen
    Pages 27-33
  6. Juha Heinonen
    Pages 34-42
  7. Juha Heinonen
    Pages 43-48
  8. Juha Heinonen
    Pages 59-67
  9. Juha Heinonen
    Pages 68-77
  10. Juha Heinonen
    Pages 78-87
  11. Juha Heinonen
    Pages 88-97
  12. Juha Heinonen
    Pages 103-108
  13. Juha Heinonen
    Pages 109-118
  14. Juha Heinonen
    Pages 119-125
  15. Back Matter
    Pages 127-141

About this book


Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. 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 purpose of this book is to communicate some of the recent work in the area while preparing the reader to study more substantial, related articles. 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 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. The material is relevant to anyone who is interested in analysis and geometry in nonsmooth settings.


Area Finite Sobolev space behavior calculus development eXist equality form inequality mapping maximum quasiconformal mapping theorem types

Authors and affiliations

  • Juha Heinonen
    • 1
  1. 1.Mathematics Department East HallUniversity of MichiganAnn ArborUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6525-2
  • Online ISBN 978-1-4613-0131-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site