Stable minimal hypersurfaces with weighted Poincar\'{e} inequality in a Riemannian manifold
Commun. Korean Math. Soc. 2014 Vol. 29, No. 1, 123-130
Printed January 31, 2014
Nguyen Dinh Sang and Nguyen Thi Thanh
Nguyen Trai street, Thanh Xuan, No. 12, Tran Phu street, Ngo Quyen district
Abstract : In this note, we investigate stable minimal hypersurfaces with weighted Poincar\'{e} inequality. We show that we still get the vanishing property without assuming that the hypersurfaces is non-totally geodesic. This generalizes a result in \cite{D-S}.
Keywords : minimal hypersurface, stability, weighted Poincar\'{e} inequality
MSC numbers : Primary 53C42, 58C40
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