Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Authors: Pierre Guerini and Alessandro Savo
Journal: Trans. Amer. Math. Soc. 356 (2004), 319-344
MSC (2000): Primary 58J50; Secondary 58J32
Published electronically: August 25, 2003
MathSciNet review: 2020035
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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 Information

Pierre Guerini
Affiliation: Institut für Mathematik, Universität Zürich Irchel, Winterthurerstrasse 90, CH-8057 Zürich, Switzerland
Email: pguerini@math.unizh.ch

Alessandro Savo
Affiliation: Dipartimento di Metodi e Modelli Matematici, Università di Roma I La Sapienza, Via Antonio Scarpa 16, 00161 Roma, Italy
Email: savo@dmmm.uniroma1.it

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03336-1
Keywords: Hodge Laplacian, eigenvalues, gaps, convex manifolds
Received by editor(s): January 13, 2003
Published electronically: August 25, 2003
Article copyright: © Copyright 2003 American Mathematical Society