A Bonnesen-style inradius inequality in 3-space
type: Item
instance of: scholarly article
title: A Bonnesen-style inradius inequality in 3-space
zbMATH Open document ID: 0658.52005
author: J. R. Sangwine-Yager
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let K be a convex body in 3-dimensional Euclidean space, and let V, S, (1/2\(\pi)\)M, and r denote the volume, surface area, mean-width and inradius of K. The author establishes the inequality \[ V - rS + \frac{2}{3}r^ 2M \leq 0 \] with equality if and only if K is a cap body of a ball. A cap body of a ball is the convex hull of the ball and countably many points exterior to it such that the line segment joining any two of these points intersects the ball. The above inequality is obtained as a consequence of an inequality providing a lower bound for the volume of an inner parallel body of K.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A15
Mathematics Subject Classification ID: 51M25
zbMATH DE Number: 4075949
zbMATH Keywords: convex body in 3-dimensional Euclidean space
zbMATH Keywords: volume
zbMATH Keywords: surface area
zbMATH Keywords: mean- width
zbMATH Keywords: inradius
reviewed by: August Florian
MaRDI profile type: Publication
full work available at URL: pjm.1988.134.173
OpenAlex ID: W2046316089
DOI: 10.2140/PJM.1988.134.173
description: scientific article; zbMATH DE number 4075949