Compactness criteria for Riemannian manifolds with compact unstable minimal hypersurfaces
type: Item
instance of: scholarly article
title: Compactness criteria for Riemannian manifolds with compact unstable minimal hypersurfaces
zbMATH Open document ID: 0701.53062
author: Kazuo Akutagawa
published in: Tsukuba Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author proves an Ambrose-type theorem as follows: Let N be a complete Riemannian manifold with a compact embedded unstable minimal hypersurface M. Suppose that there exists a positive constants \(s_ 0\) such that along each unit speed geodesic \(\gamma\) : \([0,\infty)\to N\) emanating from each point in the tubular neighborhood \(U_{s_ 0}(M):=\{g\in N;\quad dist_ N(g,M)<s_ 0\}\) the Ricci curvature satisfies \(\liminf_{r\to \infty}\int^{r}_{0}Ric_ N(d\gamma /dt,d\gamma /dt)dt\geq 0.\) Then N is compact. For other Ambrose-type theorems see \textit{G. J. Galloway} [Proc. Am. Math. Soc. 84, 106-110 (1982; Zbl 0484.53032)].
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4149105
zbMATH Keywords: Ambrose-type theorem
zbMATH Keywords: minimal hypersurface
zbMATH Keywords: Ricci curvature
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496161172
OpenAlex ID: W271975733
Wikidata QID: Q115233582
DOI: 10.21099/TKBJM/1496161172
description: scientific article; zbMATH DE number 4149105