ENGLISH

Analytic Capacity, Rectifiability, Menger Curvature, and Cauchy Integral

By Pajot H. M.

Book information

Publisher
Springer
Year
2003
Language
english
Format
RAR
Filesize
1 MB (1544427 bytes)
Series
Lecture Notes in Mathematics 1799
Pages
140\0
Library
mexmat
Time added
2009-07-20 03:45:11

Description

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.

Similar books