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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A class of 3-dimensional manifolds
with bounded first eigenvalue on 1-forms


Author: Giovanni Gentile
Journal: Proc. Amer. Math. Soc. 127 (1999), 2755-2758
MSC (1991): Primary 53C20; Secondary 58G25
DOI: https://doi.org/10.1090/S0002-9939-99-04916-3
Published electronically: April 23, 1999
MathSciNet review: 1610893
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Abstract: Let $(P,g)$ be the framebundle over an oriented, $C^\infty$ Riemannian surface $S$. Denote by $\lambda-{1,1}(P,g)$ the first nonzero eigenvalue of the Laplace operator acting on differential forms of degree 1. We prove that $\lambda _{1,1}(P,g)\le c$ for all $(P,g)$ with canonical metrics $g$ of volume 1.


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Additional Information

Giovanni Gentile
Affiliation: Department of Mathematics, ETH-Zentrum, HG G34, CH 8092 Zurich, Switzerland

DOI: https://doi.org/10.1090/S0002-9939-99-04916-3
Received by editor(s): December 1, 1997
Published electronically: April 23, 1999
Communicated by: Peter Li
Article copyright: © Copyright 1999 American Mathematical Society