Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] /

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.

Bibliographic Details

Main Authors:	Pajot, Hervé. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002
Subjects:	Mathematics., Mathematical analysis., Analysis (Mathematics)., Fourier analysis., Functions of complex variables., Measure theory., Geometry., Analysis., Measure and Integration., Functions of a Complex Variable., Fourier Analysis.,
Online Access:	http://dx.doi.org/10.1007/b84244
Tags:	Add Tag No Tags, Be the first to tag this record!