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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 56 NO.2 / (2004))
On Stable Complete Hypersurfaces With Vanishing $r$-Mean Curvature
Manfredo Do Carmo and Maria F.Elbert,
Pages. 155-162
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 on complete stable hypersurface on 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 immer-sion is proper and the total curvature is finite.
Contents 1. Introduction
2. Proof of Theorem 1.1.
Key words Stability, $r$-mean curvature, complete, finite total curvature.
Mathmatical Subject Classification 53C42