Towards Conformal Capacities in Euclidean Spaces

الأصل · EN

This paper addresses the so-called conformal capacities in Rⁿ, n≥ 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.