Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral

  • Authors
  • Hervé Pajot

Part of the Lecture Notes in Mathematics book series (LNM, volume 1799)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Hervé Pajot
    Pages 1-15
  3. Hervé Pajot
    Pages 29-54
  4. Hervé Pajot
    Pages 81-103
  5. Hervé Pajot
    Pages 115-118
  6. Hervé Pajot
    Pages 119-119
  7. Back Matter
    Pages 119-125

About this book

Introduction

Based on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem.

Keywords

Cauchy integral Complex analysis Singular integral analysis analytic capacity harmonic analysis menger curvature rectifiability singular integral operators

Bibliographic information

  • DOI https://doi.org/10.1007/b84244
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-00001-3
  • Online ISBN 978-3-540-36074-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book