Homothetic floating bodies
type: Item
instance of: scholarly article
title: Homothetic floating bodies
zbMATH Open document ID: 0802.52002
DOI: 10.1007/BF01264033
published in: Geometriae Dedicata
publication date: 1994-05-18T00:00:00Z
review text: The convex floating body \(K_ \delta\) of a convex body \(K\) in \(E^ d\) is the intersection of all halfspaces whose hyperplanes cut off a set of volume \(\delta\) from \(K\). Authors prove that \(K\) is an ellipsoid if there is a sequence \(\{\delta_ k\}_{k \in N}\) converging to 0 such that each \(K_{\delta_ k}\) is homothetic to \(K\) with respect to the same center of homothety.
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 569272
zbMATH Keywords: floating body
zbMATH Keywords: convex body
zbMATH Keywords: ellipsoid
zbMATH Keywords: homothety
author: Carsten Schütt
author: Elisabeth M. Werner
reviewed by: Christoph Schulz
MaRDI profile type: Publication
cites work: Blaschke’s rolling theorem in 𝑅ⁿ
cites work: Characterizations of ellipsoids by section-centroid location
cites work: A geometric property of the boundary of symmetric convex bodies and convexity of flotation surfaces
cites work: The volume of the intersection of a convex body with its translates
cites work: The convex floating body.
cites work: The convex floating body of almost polygonal bodies
full work available at URL: https://doi.org/10.1007/bf01264033
OpenAlex ID: W2032231817
description: scientific article; zbMATH DE number 569272