Eigenvalues of the Laplacian on forms

Dodziuk, Jozef

doi:10.1090/S0002-9939-1982-0656119-2

Eigenvalues of the Laplacian on forms
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by Jozef Dodziuk

Proc. Amer. Math. Soc. 85 (1982), 437-443

DOI: https://doi.org/10.1090/S0002-9939-1982-0656119-2

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Abstract:

Some bounds for eigenvalues of the Laplace operator acting on forms on a compact Riemannian manifold are derived. In case of manifolds without boundary we give upper bounds in terms of the curvature, its covariant derivative and the injectivity radius. For a small geodesic ball upper and lower bounds of eigenvalues in terms of bounds of sectional curvature are given.

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