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Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

Paperback

Series: Lecture Notes in Mathematics, Book 1799

Medical ReferenceCalculusGeneral Mathematics

ISBN10: 3540000011
ISBN13: 9783540000013
Publisher: Springer
Published: Nov 26 2002
Pages: 119
Weight: 0.45
Height: 0.30 Width: 6.14 Depth: 9.21
Language: English
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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