Asian Journal of Mathematics

Volume 22 (2018)

Number 5

Exploiting log-capacity in convex geometry

Pages: 955 – 980

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n5.a8

Author

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

35J92, 53A30

Full Text (PDF format)

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