On stable complete hypersurfaces with vanishing r-mean curvature

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概要

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• 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.

著者

• Do Carmo

  Instituto Nacional De Matemaica Pura E Aplicada (impa)

• Elbert Maria

  Instituto de Matematica, UFRJ

• Elbert Maria

  Instituto De Matematica Ufrj

関連論文

• On stable complete hypersurfaces with vanishing r-mean curvature

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