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

2025/05/25 by Artstein-Avidan, Shiri, Chor, Arnon
#52A40 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2505.19172

Abstract

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 (n)/(n+1), and that a Santaló-type inequality holds: Ω^c(K) Ω^c(K^c) ≤ Ω^c((1)/(2) B₂ⁿ)². We also produce some more intricate inequalities involving the surface area.

Citations

• An in-depth study of ball-bodies
• Floating bodies for ball-convex bodies
• Isometries of the class of ball-bodies
• A full classification of the isometries of the class of ball-bodies
• Selected topics from the theory of intersections of balls

Related

• Extremal affine surface areas in a functional setting
• The Santalo-regions of a convex body
• A general geometric construction for affine surface area
• On the p-affine surface area
• Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory