UZH-Logo

Maintenance Infos

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.

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.

Citations

8 citations in Web of Science®
8 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

75 downloads since deposited on 29 Nov 2010
32 downloads since 12 months
Detailed statistics

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:05 Apr 2016 13:24
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
Permanent URL: https://doi.org/10.5167/uzh-21799

Download

[img]
Preview
Filetype: PDF
Size: 390kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations