Some Bonnesen-style inequalities for higher dimensions
type: Item
instance of: scholarly article
title: Some Bonnesen-style inequalities for higher dimensions
zbMATH Open document ID: 1272.52006
author: Yan Hua Du
author: Fei Cheng
author: Jiazu Zhou
publication date: 2013-03-12T00:00:00Z
review text: The authors consider the higher dimensional Bonnesen-style inequalities. They prove the following: If \(K\) is a domain in the Euclidean space \(\mathbb{R}^n\) with surface area \(S\) and volume \(V\) and \(K^{*}\) is the convex hull of \(K\) of the surface area \(S^{*}\) and volume \(V^{*}\), then for \(S\geq S^{*}\) \[ S^n-n^n \omega_nV^{n-1} \geq (S-S^{*})^n \quad\text{ and }\quad S^n-n^n \omega_nV^{n-1} \geq C \omega_n (V^{*}-V)^{n-1}, \] where \(C\) is a constant and \(\omega_n\) is the volume of the unit ball of \(\mathbb{R}^n\). Each equality holds when \(K\) is an \(n\)-ball.
reviewed by: Monika Nowicka
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 6143614
zbMATH Keywords: convex domain
zbMATH Keywords: isoperimetric deficit
zbMATH Keywords: isoperimetric inequality
zbMATH Keywords: Bonnesen-style inequality
MaRDI profile type: Publication
full work available at URL: s10114-012-9657-6
OpenAlex ID: W2068977245
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DOI: 10.1007/S10114-012-9657-6
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6143614