Analytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral

• Main Author: Pajot, Hervé M. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1799
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Geometry.; Measure theory.; Functions of complex variables.; Fourier analysis.; Analysis.; Measure and Integration.; Functions of a Complex Variable.; Fourier Analysis.
• Physical Description: VIII, 119 p. online resource.
• ISBN: 9783540360742
• ISSN: 0075-8434 ;
• DOI: 10.1007/b84244

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.