Abstract
A form of Bernstein theorem states that a complete stable minimal surface in euclidean space is a plane. A generalization of this statement is that there exists no complete stable hypersurface of an $n$-euclidean space with vanishing $(n-1)$-mean curvature and nowhere zero Gauss-Kronecker curvature. We show that this is the case, provided the immersion is proper and the total curvature is finite.
Citation
Maria F. Elbert. Manfredo do Carmo. "On stable complete hypersurfaces with vanishing {$r$}-mean curvature." Tohoku Math. J. (2) 56 (2) 155 - 162, 2004. https://doi.org/10.2748/tmj/1113246548
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