English

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.

Keywords

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

R2 v1 2026-06-23T10:43:14.241Z