Journal ArticleDOI
Kinematische Berührmaße für konvexe Körper und Integralrelationen für Oberflächenmaße
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This article is published in Mathematische Annalen.The article was published on 1975-10-01. It has received 42 citations till now.read more
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Convex bodies : the Brunn-Minkowski theory
TL;DR: Inequalities for mixed volumes 7. Selected applications Appendix as discussed by the authors ] is a survey of mixed volumes with bounding boxes and quermass integrals, as well as a discussion of their applications.
Book ChapterDOI
Valuations on convex bodies
Peter McMullen,Rolf Schneider +1 more
TL;DR: Hadwiger's celebrated characterizations of the quermassintegrals by the valuation and other properties were the culmination of a series of papers on valuations and at the same time the starting point for various subsequent investigations of functionals with similar properties as discussed by the authors.
Book ChapterDOI
Valuations and Dissections
TL;DR: In this paper, the authors discuss the state of knowledge of valuations and dissections and discuss the relationship between polytope algebra and the polytopes of a given algebra.
Journal ArticleDOI
Curvature measures of convex bodies
TL;DR: In this article, the curvature measure of order m was shown to measure the affine subspaces of codimension m+1 which touch the convex body of the body.
Book ChapterDOI
Boundary structure and curvature of convex bodies
TL;DR: A survey of the implications of convexity of a point set on the structure of its boundary can be found in this article, where the authors have tried to collect the known results which describe, or are connected with, local geometric properties of the boundary of a convex body.
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Vorlesungen über Inhalt, Oberfläche und Isoperimetrie
TL;DR: In this article, a vorliegende Buch vereinigt in seinen wesentlichen Teilen den Stoff verschiedener Vorlesungen liber Inhaltstheorie, isoperimetrische Probleme and liber konvexe Karper and allgemeine Integralgeometrie, which ich im Laufe der letten yearre an der Universitat Bern gehalten habe.
Journal ArticleDOI
Ein Approximationssatz für konvexe Körper
TL;DR: In this paper, it was shown that a convex body in n-dimensional Euclidean space can be approximated by a sequence of smooth convex bodies in such a way that the principal radii of curvature converge in a certain sense.