NDLI: Weakly stable constant mean curvature hypersurfaces

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Weakly stable constant mean curvature hypersurfaces

Content Provider	Springer Nature Link
Author	Xu, Hong wei Fu, Hai ping
Copyright Year	2009
Abstract	Let M $^{ n }$ be an n-dimensional complete noncompact oriented weakly stable constant mean curvature hypersurface in an (n+1)-dimensional Riemannian manifold N $^{ n+1}$ whose (n− 1)th Ricci curvature satisfying Ric (n−1) N ≥(n−1)c. Denote by H and φ the mean curvature and the trace-free second fundamental form of M respectively. If \|ϕ\|$^{2}$ − (n − 2)√n(n − 1)\|H\|\|ϕ\| + n(2n − 1)(H $^{2}$ + c) ≥ 0, then M does not admit nonconstant bounded harmonic functions with finite Dirichlet integral. In particular, if N has bounded geometry and c + H $^{2}$ > 0, then M must have only one end.
Ending Page	126
Page Count	8
Starting Page	119
File Format	PDF
ISSN	10051031
e-ISSN	19930445
Journal	Applied Mathematics-A Journal of Chinese Universities
Issue Number	1
Volume Number	24
Language	English
Publisher	SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
Publisher Date	2009-03-23
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	ends constant mean curvature Mathematics Applications of Mathematics weakly stable hypersurface
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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