A representation for volume involving interior reach
type: Item
instance of: scholarly article
title: A representation for volume involving interior reach
zbMATH Open document ID: 0788.52006
DOI: 10.1007/BF01459722
author: J. R. Sangwine-Yager
published in: Mathematische Annalen
publication date: 1994-05-26T00:00:00Z
full work available at URL: https://eudml.org/doc/165158
review text: The interior reach at a boundary point of an \(n\)-dimensional convex body is the radius of the largest ball contained within the body which also includes the boundary point. The author shows: The volume of a convex body may be represented as an alternating sum of integrals of powers of the interior reach function. Each integral is over the boundary of the body and the integration is with respect to the appropriate Federer curvature measure.
Mathematics Subject Classification ID: 52A38
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 537304
zbMATH Keywords: \(n\)-dimensional convex body
zbMATH Keywords: interior reach
zbMATH Keywords: volume
zbMATH Keywords: Federer curvature measure
MaRDI profile type: Publication
cites work: On the inner parallel body of a convex body
cites work: Curvature in the Eighties
cites work: Compact hypersurfaces with constant scalar curvature and a congruence theorem
cites work: Q3862690
cites work: Bestimmung konvexer Körper durch Krümmungsmaße
cites work: Q4054306
description: scientific article; zbMATH DE number 537304