A generalization of intersection formulae of integral geometry
type: Item
instance of: scholarly article
title: A generalization of intersection formulae of integral geometry
zbMATH Open document ID: 0909.52002
DOI: 10.1023/A:1004976306108
author: Stefan Glasauer
published in: Geometriae Dedicata
publication date: 1999-03-29T00:00:00Z
review text: The paper concerns generalizations of two intersection formulae for curvature measures of convex bodies: the principal kinematic formula and the Crofton formula (Theorems 1.1 and 1.2). The author proves two pairs of theorems: \{3.1, 3.2\} and \{3.3, 3.4\}. All of these theorems deal with the so-called support measures (generalized curvature measures), which are due to R. Schneider. The first pair concerns convex bodies, the second concerns elements of convex rings, i.e. finite unions of convex bodies. Theorems 3.1 and 3.3 are counterparts of the principal kinematic formula; they are proved under some additional assumption (for the so-called admissible convex bodies and, respectively, admissible elements of the convex ring). It is an open problem whether this assumption is essential. Theorems 3.2 and 3.4 are generalizations of the Crofton formula.
reviewed by: Maria Moszyńska
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A22
zbMATH DE Number: 1098494
zbMATH Keywords: convex ring
zbMATH Keywords: generalized curvature measures
zbMATH Keywords: intersection formulae
zbMATH Keywords: curvature measures
zbMATH Keywords: convex bodies
zbMATH Keywords: principal kinematic formula
zbMATH Keywords: Crofton formula
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1098494