The Santal\'o point for the Holmes-Thompson boundary area
Metric Geometry
2023-04-03 v2 Differential Geometry
Abstract
We explore the notion of Santal\'o point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is , and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit ball, we exhibit a dual Santal\'o point expressed as an average of centroids of projections of the dual body.
Cite
@article{arxiv.2012.11440,
title = {The Santal\'o point for the Holmes-Thompson boundary area},
author = {Florent Balacheff and Gil Solanes and Kroum Tzanev},
journal= {arXiv preprint arXiv:2012.11440},
year = {2023}
}
Comments
21 pages, 2 figures. We have added a new result to the paper showing that our previous uniqueness results hold without any regularity assumptions in case the two convex bodies B and K coincide. This is the content of the new Theorem 1.2