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Stable minimal hypersurfaces with weighted Poincaré inequality in a Riemannian manifold. (English) Zbl 1288.53055

In this paper, the authors investigate stable minimal hypersurfaces with weighted Poincaré inequality. They prove the vanishing property without assuming that the hypersurfaces are non-totally geodesic. This generalizes a result by Nguyen Thac Dung and K. Seo [Ann. Global Anal. Geom. 41, No. 4, 447–460 (2012; Zbl 1242.53073)].

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
58C40 Spectral theory; eigenvalue problems on manifolds

Citations:

Zbl 1242.53073
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