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- W2952502014 abstract "We give an estimate of the first eigenvalue 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." @default.
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- W2952502014 date "2011-06-03" @default.
- W2952502014 modified "2023-09-26" @default.
- W2952502014 title "Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature" @default.
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- W2952502014 doi "https://doi.org/10.48550/arxiv.1106.0693" @default.
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