A Maximum Problem of S.-T. Yau for Variational p-Capacity

Abstract

Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in ${\mathbb{R}}^{n\ge 2}$ as an sharp upper bound of the variational $(1,n)\ni p$-capacity radius, this paper settles a restriction/variant of S.-T. Yau's \cite[Problem 59]{Yau} from the surface area to the variational $p$-capacity whose limit as $p\to 1$ actually induces the surface area.

17 pages, accepted by Advances in Geometry, 2016

Cited by in corpus (2)

• Towards Conformal Capacities in Euclidean Spaces
• Geometric Capacity Potentials on Convex Plane Rings