JournalscmhVol. 76 , No. 1DOI 10.1007/s000140050153

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

  • Alain R. Veeravalli

    Université d'Evry - Val d'Essonne, France
On the first Laplacian eigenvalue and the center of gravity of compact hypersurfaces cover

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.