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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Eigenvalues of the Laplacian on forms
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by Jozef Dodziuk PDF
Proc. Amer. Math. Soc. 85 (1982), 437-443 Request permission

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.
References
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • 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