Unrectifiable 1-sets have vanishing analytic capacity.

Título inglés Unrectifiable 1-sets have vanishing analytic capacity.
Título español Los conjuntos unidimensionales no rectificables tienen la capacidad analítica nula.
Autor/es David, Guy
Organización Dep. Math. Univ. Paris-Sud, Orsay, Francia
Revista 0213-2230
Publicación 1998, 14 (2): 369-479, 32 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés We complete the proof of a conjecture of Vitushkin that says that if E is a compact set in the complex plane with finite 1-dimensional Hausdorff measure, then E has vanishing analytic capacity (i.e., all bounded anlytic functions on the complement of E are constant) if and only if E is purely unrectifiable (i.e., the intersection of E with any curve of finite length has zero 1-dimensional Hausdorff measure). As in a previous paper with P. Mattila, the proof relies on a rectifiability criterion using Menger curvature, and an extension of a construction of M. Christ. The main new part is a generalization of the T(b)-theorem to some spaces that are non necessarily of homogeneous type.
Clasificación UNESCO 120217
Palabras clave español Conjuntos medibles ; Espacio de Hausdorff ; Unidimensional ; Funciones analíticas
Código MathReviews MR1654535
Código Z-Math Zbl 0913.30012
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