Towards Conformal Capacities in Euclidean Spaces

Abstract

This paper addresses the so-called conformal capacities in ${\mathbb{R}}^n$, $n\ge 3$, through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamananmurthy-Fuglede respectively) and studying their associated iso-capacitary inequalities with connection to half-diameter, mean-width, mean-curvature and ADM-mass, Hadamard type variational formula, Minkowski type problem, and Yau type problem.

33 pages

References in corpus (2)

• A Maximum Problem of S.-T. Yau for Variational p-Capacity
• Quantitative stability in the isodiametric inequality via the isoperimetric inequality