An area estimate for slices of strictly convex hypersurfaces
type: Item
instance of: scholarly article
title: An area estimate for slices of strictly convex hypersurfaces
zbMATH Open document ID: 0549.53003
DOI: 10.1007/BF00151500
author: Rita Saerens
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: The following theorem is proved. Let D be a compact, strictly convex hypersurface (with positive curvatures) in \({\mathbb{R}}^ n\) (\(n\geq 3)\) of class \(C^ 2\) and let M be the part of D between two parallel hyperplanes distance \(\epsilon\) apart. For \(\epsilon\) sufficiently small, the area of M is bounded from above by \(C\epsilon\), where C is a constant depending only on D. The proof proceeds by direct computation and estimation.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C45
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 3876090
zbMATH Keywords: upper bound
zbMATH Keywords: convex hypersurface
zbMATH Keywords: area
reviewed by: Rolf Schneider
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00151500
OpenAlex ID: W2000315553
description: scientific article; zbMATH DE number 3876090