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 ∫0 1 r−3 h(r)2 dr < ∞, 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.
@article{urn:eudml:doc:41245,
title = {On the analytic capacity and curvature of some Cantor sets with non-$\sigma$-finite length.},
journal = {Publicacions Matem\`atiques},
volume = {40},
year = {1996},
pages = {195-204},
mrnumber = {MR1397014},
zbl = {0888.30026},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41245}
}
Mattila, Pertti. On the analytic capacity and curvature of some Cantor sets with non-σ-finite length.. Publicacions Matemàtiques, Tome 40 (1996) pp. 195-204. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41245/