Asian Journal of Mathematics

Volume 22 (2018)

Number 5

Exploiting log-capacity in convex geometry

Pages: 955 – 980



Jie Xiao (Department of Mathematics and Statistics, Memorial University, St. John’s, Newfoundland, Canada)


This article is devoted to an exploitation of the log-capacity for convex bodies — especially its connections to volume-radius, mean-width, Hadamard-type variational formula, Minkowski-type problem, and Yau-type problem.


log-capacity, volume-radius, mean-width, Hadamard-type variation, Minkowski-type problem, Yau-type problem

2010 Mathematics Subject Classification

35J92, 53A30

This project was in part supported by MUN’s University Research Professorship (208227463102000).

Received 29 December 2015

Accepted 15 December 2016

Published 9 November 2018