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Analytic Capacity, Rectifiability, Menger Curvature, and the Cauchy Integral

Analytic Capacity, Rectifiability, Menger Curvature, and the Cauchy Integral

Author: 


ISBN-13: 

9783540000013


ISBN: 

3540000011


Publisher:  Springer
Summary: 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 b...etween 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 Painlevè problem. [read more]

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Analytic Capacity, Rectifiability, Menger Curvature, and the Cauchy Integral

ISBN-13: 9783540000013


ISBN: 3540000011


Publisher: Springer
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