Towards Conformal Capacities in Euclidean Spaces

2013/09/14 by Jie Xiao, Xiao, Jie
Mathematics · #35J92 #53A30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:35J92 #msc:53A30

paper · pdf · doi:10.48550/arxiv.1309.3648

33 pages

arxiv created 2013/09/14 · arxiv updated 2013/09/17

Abstract

This paper addresses the so-called conformal capacities in \mathbb 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.

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