Isocapacity Estimates for Hessian Operators

Through a new powerful potential-theoretic analysis, this paper is devoted to discovering the geometrically equivalent isocapacity forms of Chou-Wang’s Sobolev type inequality and Tian-Wang’s Moser-Trudinger type inequality for the fully nonlinear $1\le k\le n\mathrm{/}2$ Hessian operators.