On the analytic capacity and curvature of some Cantor sets with non-σ-finite length.

Mattila, Pertti. "On the analytic capacity and curvature of some Cantor sets with non-σ-finite length.." Publicacions Matemàtiques 40.1 (1996): 195-204. <http://eudml.org/doc/41245>.

@article{Mattila1996,
abstract = {We show that if a Cantor set E as considered by Garnett in [G2] has positive Hausdorff h-measure for a non-decreasing function h satisfying ∫01 r−3 h(r)2 dr &lt; ∞, 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.},
author = {Mattila, Pertti},
journal = {Publicacions Matemàtiques},
keywords = {Funciones analíticas; Operadores integrales; Integral de Cauchy; Variable compleja; Medidas de Borel; Hausdorff measure; Cantor sets; Menger three-points curvature},
language = {eng},
number = {1},
pages = {195-204},
title = {On the analytic capacity and curvature of some Cantor sets with non-σ-finite length.},
url = {http://eudml.org/doc/41245},
volume = {40},
year = {1996},
}

TY - JOUR
AU - Mattila, Pertti
TI - On the analytic capacity and curvature of some Cantor sets with non-σ-finite length.
JO - Publicacions Matemàtiques
PY - 1996
VL - 40
IS - 1
SP - 195
EP - 204
AB - We show that if a Cantor set E as considered by Garnett in [G2] has positive Hausdorff h-measure for a non-decreasing function h satisfying ∫01 r−3 h(r)2 dr &lt; ∞, 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.
LA - eng
KW - Funciones analíticas; Operadores integrales; Integral de Cauchy; Variable compleja; Medidas de Borel; Hausdorff measure; Cantor sets; Menger three-points curvature
UR - http://eudml.org/doc/41245
ER -