Some inequalities of isoperimetric type for the c-affine surface area

Fuente: arXiv
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Main Authors: Artstein-Avidan, Shiri, Chor, Arnon
Format: Preprint
Published: 2025
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author Artstein-Avidan, Shiri
Chor, Arnon
author_facet Artstein-Avidan, Shiri
Chor, Arnon
contents We study the c-affine surface area $Ω^c$, recently introduced by Schütt, Werner and Yalikun. We show that on the class of ball-bodies, $Ω^c$ is maximized by a ball of radius $\frac{n}{n+1}$, and that a Santaló-type inequality holds: $Ω^c(K) Ω^c(K^c) \leq Ω^c(\frac{1}{2} B_2^n)^2$. We also produce some more intricate inequalities involving the surface area.
format Preprint
id arxiv_https___arxiv_org_abs_2505_19172
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Some inequalities of isoperimetric type for the c-affine surface area
Artstein-Avidan, Shiri
Chor, Arnon
Metric Geometry
52A40
We study the c-affine surface area $Ω^c$, recently introduced by Schütt, Werner and Yalikun. We show that on the class of ball-bodies, $Ω^c$ is maximized by a ball of radius $\frac{n}{n+1}$, and that a Santaló-type inequality holds: $Ω^c(K) Ω^c(K^c) \leq Ω^c(\frac{1}{2} B_2^n)^2$. We also produce some more intricate inequalities involving the surface area.
title Some inequalities of isoperimetric type for the c-affine surface area
topic Metric Geometry
52A40
url https://arxiv.org/abs/2505.19172