On the analytic capacity and curvature of some Cantor sets with non-σ-finite length.
Pertti Mattila (1996)
Publicacions Matemàtiques
Similarity:
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 ∫ r h(r) 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.