Q1103890
type: Item
instance of: scholarly article
title: Une relation entre diamètre extrinsèque, intégrale de la courbure de Gauss et inradius pour les hypersurfaces localement convexes d'un espace euclidien. (A relation between external diameter, Gaussian curvature integral and inradius for locally convex hypersurfaces of a Euclidean space)
zbMATH Open document ID: 0646.53056
DOI: 10.1007/BF01159811
author: François Labourie
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183750
review text: For locally convex hypersurfaces (with boundary) in Euclidean n-space it is shown that the spherical image contains a half-sphere if \(r\geq \sqrt{2}d\) where r is the intrinsic inradius and d the extrinsic diameter.
Mathematics Subject Classification ID: 53C45
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 4054521
zbMATH Keywords: locally convex hypersurfaces
zbMATH Keywords: spherical image
zbMATH Keywords: inradius
zbMATH Keywords: diameter
MaRDI profile type: Publication
cites work: AN ESTIMATE FROM BELOW FOR THE SPATIAL DIAMETER OF A SURFACE IN TERMS OF ITS INTRINSIC RADIUS AND CURVATURE
cites work: Partial Differential Relations
cites work: Bonnesen-Style Isoperimetric Inequalities
cites work: Q4064107
OpenAlex ID: W1973808803
label: Une relation entre diamètre extrinsèque, intégrale de la courbure de Gauss et inradius pour les hypersurfaces localement convexes d'un espace euclidien. (A relation between external diameter, Gaussian curvature integral and inradius for locally convex hypersurfaces of a Euclidean space)
description: scientific article; zbMATH DE number 4054521