English

Isoperimetric relations for inner parallel bodies

Metric Geometry 2019-10-15 v1

Abstract

We analyze aspects of the behavior of the family of inner parallel bodies of a convex body for the isoperimetric quotient and deficit of arbitrary quermassintegrals. By means of technical boundary properties of the so-called form body of a convex body and similar constructions for inner parallel bodies, we point out an erroneous use of a relation between the latter bodies in two different works. We correct these results, limiting them to convex bodies having a very precise boundary structure.

Keywords

Cite

@article{arxiv.1910.05367,
  title  = {Isoperimetric relations for inner parallel bodies},
  author = {María A. Hernández Cifre and Eugenia Saorín Gómez},
  journal= {arXiv preprint arXiv:1910.05367},
  year   = {2019}
}

Comments

13 pages, 1 figure

R2 v1 2026-06-23T11:41:29.930Z