Convex hypersurfaces with pinched second fundamental form
type: Item
instance of: scholarly article
title: Convex hypersurfaces with pinched second fundamental form
zbMATH Open document ID: 0843.53002
author: Richard S. Hamilton
published in: Communications in Analysis and Geometry
publication date: 1995-11-26T00:00:00Z
review text: The following Theorem is proved: Let \(M^n\) be a smooth strictly convex complete hypersurface bounding a region in \(\mathbb{R}^{n+1}\). Suppose that its second fundamental form is \(\varepsilon\)-pinched in the sense the \(H_{ij} \geq \varepsilon Hg_{ij}\), where \(g_{ij}\) is the induced Riemannian metric, \(H_{ij}\) the second fundamental form, and its trace \(H\) is the mean curvature, for some \(\varepsilon>0\). Then \(M^n\) is compact.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 820214
zbMATH Keywords: Gauss map
zbMATH Keywords: pinching
zbMATH Keywords: strictly convex hypersurfaces
zbMATH Keywords: second fundamental form
zbMATH Keywords: mean curvature
MaRDI profile type: Publication
full work available at URL: cag.1994.v2.n1.a10
OpenAlex ID: W2622334219
DOI: 10.4310/CAG.1994.V2.N1.A10
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description: scientific article; zbMATH DE number 820214