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 |
Acceso al artículo completo |