Analytic capacity, rectifiability, Menger curvature and the Cauchy integral / Hervé Pajot

Auteur: Pajot, Hervé (1967-) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 1799Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, 2002Description: 1 vol. (XII-118 p.) ; 24 cm ISBN: 3540000011 ; br. Résumé: This is an excellent book on a subject that has experienced an impressive sequence of striking results in the last decade. It comes at the right time and will certainly be a standard source and reference for many years. The book deals with Painlevé's problem and its relationships with geometric measure theory, the Calderón-Zygmund theory of the Cauchy kernel in the plane and curvature. The notion of curvature relevant here is Menger's curvature associated to three points in the plane, that is, the inverse of the radius of the circle passing through the three points. ... (MathSciNet).Bibliographie: Bibliogr. p. [115]-118.Index. Sujets MSC: 28A75 Measure and integration -- Classical measure theory -- Length, area, volume, other geometric measure theory
30C85 Functions of a complex variable -- Geometric function theory -- Capacity and harmonic measure in the complex plane
42B20 Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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Bibliogr. p. [115]-118.Index

This is an excellent book on a subject that has experienced an impressive sequence of striking results in the last decade. It comes at the right time and will certainly be a standard source and reference for many years.
The book deals with Painlevé's problem and its relationships with geometric measure theory, the Calderón-Zygmund theory of the Cauchy kernel in the plane and curvature. The notion of curvature relevant here is Menger's curvature associated to three points in the plane, that is, the inverse of the radius of the circle passing through the three points. ... (MathSciNet)

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