Analytic capacity and the Painlevé Problem

Hervé Pajot

Séminaire Bourbaki (2003-2004)

  • Volume: 46, page 301-328
  • ISSN: 0303-1179

Abstract

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The Painlevé problem consists in finding a geometric characterization of removable sets for bounded analytic functions in the complex plane. This problem of complex analysis has known very striking results in the last years. These progress are based on recent developments in real analysis and geometric measure theory. In this talk, we will present and discuss a solution to the Painlevé problem proposed by X. Tolsa in terms of Menger curvature.

How to cite

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Pajot, Hervé. "Capacité analytique et le problème de Painlevé." Séminaire Bourbaki 46 (2003-2004): 301-328. <http://eudml.org/doc/252170>.

@article{Pajot2003-2004,
abstract = {Le problème de Painlevé consiste à trouver une caractérisation géométrique des sous-ensembles du plan complexe qui sont effaçables pour les fonctions holomorphes bornées. Ce problème d’analyse complexe a connu ces dernières années des avancées étonnantes, essentiellement grâce au dévelopement de techniques fines d’analyse réelle et de théorie de la mesure géométrique. Dans cet exposé, nous allons présenter et discuter une solution proposée par X. Tolsa en termes de courbure de Menger au problème de Painlevé.},
author = {Pajot, Hervé},
journal = {Séminaire Bourbaki},
keywords = {analytic capacity; rectifiability; Cauchy integral; Menger curvature; uniformly rectifiable sets},
language = {fre},
pages = {301-328},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Capacité analytique et le problème de Painlevé},
url = {http://eudml.org/doc/252170},
volume = {46},
year = {2003-2004},
}

TY - JOUR
AU - Pajot, Hervé
TI - Capacité analytique et le problème de Painlevé
JO - Séminaire Bourbaki
PY - 2003-2004
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 46
SP - 301
EP - 328
AB - Le problème de Painlevé consiste à trouver une caractérisation géométrique des sous-ensembles du plan complexe qui sont effaçables pour les fonctions holomorphes bornées. Ce problème d’analyse complexe a connu ces dernières années des avancées étonnantes, essentiellement grâce au dévelopement de techniques fines d’analyse réelle et de théorie de la mesure géométrique. Dans cet exposé, nous allons présenter et discuter une solution proposée par X. Tolsa en termes de courbure de Menger au problème de Painlevé.
LA - fre
KW - analytic capacity; rectifiability; Cauchy integral; Menger curvature; uniformly rectifiable sets
UR - http://eudml.org/doc/252170
ER -

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