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).
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Uncontrolled Keywords: | Hodge Laplacian, eigenvalues, gaps, convex manifolds |
| Language: | English |
| Date: | 2004 |
| Deposited On: | 29 Nov 2010 16:26 |
| Last Modified: | 23 Jan 2022 14:36 |
| Publisher: | American Mathematical Society |
| ISSN: | 0002-9947 |
| Additional Information: | First published in [Trans. Amer. Math. Soc. 356 (2004)], published by the American Mathematical Society |
| OA Status: | Hybrid |
| Publisher DOI: | https://doi.org/10.1090/S0002-9947-03-03336-1 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2020035 |
Guerini, P