On convex bodies that are characterizable by volume function
Metric Geometry
2019-08-09 v1
Abstract
The "old-new" concept of convex-hull function was investigated by several authors in the last seventy years. A recent research on it led to some other volume functions as the covariogram function, the widthness function or the so-called brightness functions, respectively. A very interesting fact that there are many long-standing open problems connected with these functions whose serious investigation closed before the "age of computers". In this survey, we concentrate only on the three-dimensional case, we will mention the most important concepts, statements, and problems.
Cite
@article{arxiv.1908.03196,
title = {On convex bodies that are characterizable by volume function},
author = {Ákos G. Horváth},
journal= {arXiv preprint arXiv:1908.03196},
year = {2019}
}
Comments
16 pages, 9 figures. arXiv admin note: text overlap with arXiv:0805.1605 by other authors