Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral
Hervé Pajot (auth.)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.
Категорії:
Рік:
2002
Видання:
1
Видавництво:
Springer-Verlag Berlin Heidelberg
Мова:
english
Сторінки:
119
ISBN 10:
3540000011
ISBN 13:
9783540000013
Серії:
Lecture Notes in Mathematics 1799
Файл:
PDF, 710 KB
IPFS:
,
english, 2002