Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral
Author :
Publisher : Springer
Total Pages : 133
Release :
ISBN-10 : 9783540360742
ISBN-13 : 3540360743
Rating : 4/5 (743 Downloads)

Book Synopsis Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral by : Hervé M. Pajot

Download or read book Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral written by Hervé M. Pajot and published by Springer. This book was released on 2002-01-01 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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