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Tubes and eigenvalues for negatively curved manifolds
Auteur(s)
Date de parution
1993
In
Journal of Geometric Analysis
Vol.
1
No
3
De la page
1
A la page
26
Résumé
We investigate the structure of the spectrum near zero for the Laplace operator on a complete negatively curved Riemannian manifold M. If the manifold is compact and its sectional curvatures K satisfy 1 less-than-or-equal-to K < 0, we show that the smallest positive eigenvalue of the Laplacian is bounded below by a constant depending only on the volume of M. Our result for a complete manifold of finite volume with sectional curvatures pinched between -a2 and -1 asserts that the number of eigenvalues of the Laplacian between 0 and (n -1)2/4 is bounded by a constant multiple of the volume of the manifold with the constant depending on a and the dimension only.
Identifiants
Type de publication
journal article
