Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature
- Authors
- Nguyen Thac Dung; Seo, Keomkyo
- Issue Date
- Apr-2012
- Publisher
- SPRINGER
- Keywords
- Minimal hypersurface; Stability; First eigenvalue
- Citation
- ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v.41, no.4, pp 447 - 460
- Pages
- 14
- Journal Title
- ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
- Volume
- 41
- Number
- 4
- Start Page
- 447
- End Page
- 460
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/11941
- DOI
- 10.1007/s10455-011-9293-x
- ISSN
- 0232-704X
1572-9060
- Abstract
- We give an estimate of the smallest spectral value of the Laplace operator on a complete noncompact stable minimal hypersurface M in a complete simply connected Riemannian manifold with pinched negative sectional curvature. In the same ambient space, we prove that if a complete minimal hypersurface M has sufficiently small total scalar curvature then M has only one end. We also obtain a vanishing theorem for L (2) harmonic 1-forms on minimal hypersurfaces in a Riemannian manifold with sectional curvature bounded below by a negative constant. Moreover, we provide sufficient conditions for a minimal hypersurface in a Riemannian manifold with nonpositive sectional curvature to be stable.
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