On the analytic capacity and curvature of some Cantor sets with non-$\sigma$-finite length

Autores: Pertti Mattila
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 40, Nº 1, 1996, págs. 195-204
Idioma: inglés
DOI: 10.5565/publmat_40196_12
Títulos paralelos:
- Capacidad analítica y curvatura de algunos conjuntos de Cantor con longitud no-s-finita
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Resumen
- We show that if a Cantor set $E$ as considered by Garnett in \cite{G2} has positive Hausdorff $h$-measure for a non-decreasing function $h$ satisfying $\int^1_0r^{-3}\,h(r)^2\,dr<\infty$, then the analytic capacity of $E$ is positive. Our tool will be the Menger three-point curvature and Melnikov's identity relating it to the Cauchy kernel. We shall also prove some related more general results.