Open AccessOn the first Laplacian eigenvalue and the center of gravity of compact hypersurfaces
Author(s) -
Alain R. Veeravalli
Publication year - 2001
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.1007/s000140050153
Subject(s) - hypersurface , mathematics , laplace operator , eigenvalues and eigenvectors , center of gravity , mathematical analysis , center (category theory) , pure mathematics , upper and lower bounds , physics , quantum mechanics , crystallography , chemistry , management , economics
. 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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