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.

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...

Table of Contents:

• Preface
• Notations and conventions
• Some geometric measures theory
• Jones' traveling salesman theorem
• Menger curvature
• The Cauchy singular integral operator on Ahlfors-regular sets
• Analytic capacity and the Painlevé Problem
• The Denjoy and Vitushkin conjectures
• The capacity $gamma (+)$ and the Painlevé Problem
• Bibliography
• Index.