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Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

  • Book
  • © 2002

Overview

Authors:
  1. Hervé Pajot
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1799)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
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  2. 1. Some geometric measure theory

    • HervĂ© Pajot
    Pages 1-15

  3. 2. P. Jones’ traveling salesman theorem

    • HervĂ© Pajot
    Pages 17-27

  4. 3. Menger curvature

    • HervĂ© Pajot
    Pages 29-54

  5. 4. The Cauchy singular integral operator on Ahlfors regular sets

    • HervĂ© Pajot
    Pages 55-65

  6. 5. Analytic capacity and the Painlevé problem

    • HervĂ© Pajot
    Pages 67-79

  7. 6. The Denjoy and Vitushkin conjectures

    • HervĂ© Pajot
    Pages 81-103

  8. 7. The capacity \(\gamma_{ + }\) and the Painlevé Problem

    • HervĂ© Pajot
    Pages 105-114

  9. Bibliography

    • HervĂ© Pajot
    Pages 115-118

  10. Index

    • HervĂ© Pajot
    Pages 119-119

  11. Back Matter

    Pages 119-125
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Keywords

About this book

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.

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