EHML 24Apr1997 ON THE LAPLACE OPERATOR PENALIZED BY MEAN CURVATURE
نویسنده
چکیده
Let h = Pd j=1 j where the j are the principal curvatures of a d-dimensional hypersurface immersed in R, and let be the corresponding Laplace{Beltrami operator. We prove that the second eigenvalue of 1 d h is strictly negative unless the surface is a sphere, in which case the second eigenvalue is zero. In particular this proves conjectures of Alikakos and Fusco. c 1997 by the authors. Reproduction of this article, in its entirety, by any means is permitted for non{commercial purposes. Work supported by N.S.F. grant DMS-9622730 Work supported by N.S.F. grant DMS-9500840 and the MSRI 1
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