Upper Bounds for the Eigenvalues of the Laplacian on Forms on Certain Riemannian Manifolds

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J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 1, Page 87--99.

Takahashi, Junya
Upper Bounds for the Eigenvalues of the Laplacian on Forms on Certain Riemannian Manifolds
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Abstract:
We have two kinds of upper bounds of the eigenvalues of the Laplacian on forms on compact Riemannian manifolds. One is implicit in terms of the Ricci curvature and the injective radius. The other is explicit for a class of Riemannian manifolds.

Mathematics Subject Classification (1991): Primary 58G25; Secondary 58F10, 35P15, 53C20

Mathematical Reviews Number: MR1683325

Received: 1998-07-30

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