Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature |
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Authors: | Nguyen Thac Dung Keomkyo Seo |
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Affiliation: | 1.Department of Mathematics,National Tsinghua University,Hsinchu,Taiwan, R.O.C.;2.Department of Mathematics,Sookmyung Women’s University,Seoul,Korea |
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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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