Analytic capacity, rectifiability, Menger curvature and the Cauchy integral
By: Hervé Pajot.
Series: Lecture notes in mathematics -- 1799; Lecture notes in mathematics (Springer-Verlag) -- 1799.
Publisher: Springer
Published: 2002
Place of publication: Berlin; New York
Language: eng
Number of pages: 118
Subjects: Geometric measure theory; Capacity theory (Mathematics); Harmonic analysis
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.
Notes: Includes bibliographical references (p. [115]-118) and index.