First eigenvalue of the Laplace operator and mean curvature
نویسندگان
چکیده
منابع مشابه
EHML 24Apr1997 ON THE LAPLACE OPERATOR PENALIZED BY MEAN CURVATURE
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. Reproduct...
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ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 2008
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-008-0111-y