Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
by Hervé Pajot
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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Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
2002, Springer
in English
3540000011 9783540000013
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Includes bibliographical references (p. [115]-118) and index.
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