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.
Cite this article
Alain R. Veeravalli, On the first Laplacian eigenvalue and the center of gravity of compact hypersurfaces. Comment. Math. Helv. 76 (2001), no. 1, pp. 155–160DOI 10.1007/S000140050153