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Eigenvalue and gap estimates for the Laplacian acting on p-forms


Guerini, P; Savo, A (2004). Eigenvalue and gap estimates for the Laplacian acting on p-forms. Transactions of the American Mathematical Society, 356(1):319-344 (electronic).

Abstract

We study the gap of the first eigenvalue of the Hodge Laplacian acting on p-differential forms of a manifold with boundary, for consecutive values of the degree p.
We first show that the gap may assume any sign. Then we give sufficient conditions on the intrinsic and extrinsic geometry to control it. Finally, we estimate the first Hodge eigenvalue of manifolds whose boundaries have some degree of convexity.

Abstract

We study the gap of the first eigenvalue of the Hodge Laplacian acting on p-differential forms of a manifold with boundary, for consecutive values of the degree p.
We first show that the gap may assume any sign. Then we give sufficient conditions on the intrinsic and extrinsic geometry to control it. Finally, we estimate the first Hodge eigenvalue of manifolds whose boundaries have some degree of convexity.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Hodge Laplacian, eigenvalues, gaps, convex manifolds
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:21 Nov 2017 14:21
Publisher:American Mathematical Society
ISSN:0002-9947
Additional Information:First published in [Trans. Amer. Math. Soc. 356 (2004)], published by the American Mathematical Society
Publisher DOI:https://doi.org/10.1090/S0002-9947-03-03336-1
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2020035

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