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Eigenvalue and gap estimates for the Laplacian acting on  -forms
Author(s):
Pierre
Guerini;
Alessandro
Savo
Journal:
Trans. Amer. Math. Soc.
356
(2004),
319-344.
MSC (2000):
Primary 58J50;
Secondary 58J32
Posted:
August 25, 2003
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Additional information
Abstract:
We study the gap of the first eigenvalue of the Hodge Laplacian acting on  -differential forms of a manifold with boundary, for consecutive values of the degree  . 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:
10.1090/S0002-9947-03-03336-1
PII:
S 0002-9947(03)03336-1
Keywords:
Hodge Laplacian,
eigenvalues,
gaps,
convex manifolds
Received by editor(s):
January 13, 2003
Posted:
August 25, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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