Eigenvalues of the Laplacian on forms
Author:
Jozef Dodziuk
Journal:
Proc. Amer. Math. Soc. 85 (1982), 437-443
MSC:
Primary 58G25; Secondary 35P15, 58G30
DOI:
https://doi.org/10.1090/S0002-9939-1982-0656119-2
MathSciNet review:
656119
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0656119-2
Article copyright:
© Copyright 1982
American Mathematical Society
