Sang, Nguyen Dinh; Thanh, Nguyen Thi Stable minimal hypersurfaces with weighted Poincaré inequality in a Riemannian manifold. (English) Zbl 1288.53055 Commun. Korean Math. Soc. 29, No. 1, 123-130 (2014). 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)]. Reviewer: Huafei Sun (Beijing) Cited in 1 ReviewCited in 4 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 58C40 Spectral theory; eigenvalue problems on manifolds Keywords:minimal hypersurface; weighted Poincaré inequality; non-totally geodesic Citations:Zbl 1242.53073 PDFBibTeX XMLCite \textit{N. D. Sang} and \textit{N. T. Thanh}, Commun. Korean Math. Soc. 29, No. 1, 123--130 (2014; Zbl 1288.53055) Full Text: DOI Link