Analytic Capacity, Rectifiability, Menger Curvature, and Cauchy Integral [electronic resource]
- Pajot, Hervé M. 1967-
- New York : Springer Jan. 2003
- Physical Description:
- VIII, 119 p. ill 23.500 x 015.500 cm.
- Lecture Notes in Mathematics Vol. 1799
- Restrictions on Access:
- License restrictions may limit access.
- Annotation 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.
- 9783540000013 and 3540000011 (Trade Paper)
- Audience Notes:
- College Audience Springer
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