Abstract.
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.
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Received: May 22, 2000
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Veeravalli, A. On the first Laplacian eigenvalue and the center of gravity of compact hypersurfaces. Comment. Math. Helv. 76, 155–160 (2001). https://doi.org/10.1007/s000140050153
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DOI: https://doi.org/10.1007/s000140050153