Commentarii Mathematici Helvetici


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Volume 76, Issue 1, 2001, pp. 155–160
DOI: 10.1007/s000140050153

Published online: 2001-03-31

On the first Laplacian eigenvalue and the center of gravity of compact hypersurfaces

Alain R. Veeravalli[1]

(1) Université d'Evry - Val d'Essonne, France

For a closed hypersurface in a space form, this work provides some sharp upper bounds for its first positive Laplacian eigenvalue. These bounds are extrinsic as they rely on the mean curvatures and center(s) of gravity of the hypersurface.

Keywords: Hypersurface, space form, center of gravity, Laplacian eigenvalue, mean curvatures

Veeravalli Alain: On the first Laplacian eigenvalue and the center of gravity of compact hypersurfaces. Comment. Math. Helv. 76 (2001), 155-160. doi: 10.1007/s000140050153