A sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces

Details A sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces A sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces

2007-09-21

arxiv.org/abs/0709.3349v1

Mathematics

Differential Geometry

9 pages

Scientific paper

Let $M$ be a closed hypersurface in a simply connected rank-1 symmetric space
$\olm$. In this paper, we give an upper bound for the first eigenvalue of the
Laplacian of $M$ in terms of the Ricci curvature of $\olm$ and the square of
the length of the second fundamental form of the geodesic spheres with center
at the center-of-mass of $M$.

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