Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

Herve M. Pajot

Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral
Format
Paperback
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Country
Germany
Published
26 November 2002
Pages
119
ISBN
9783540000013

Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

Herve M. Pajot

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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 Painleve problem.

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