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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Riemannian metrics with large first eigenvalue on forms of degree $ p$


Authors: G. Gentile and V. Pagliara
Journal: Proc. Amer. Math. Soc. 123 (1995), 3855-3858
MSC: Primary 58G25; Secondary 35P15, 53C20
MathSciNet review: 1277111
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Abstract: Let (M, g) be a compact, connected, $ {C^\infty }$ Riemannian manifold of n dimensions. Denote by $ {\lambda _{1,p}}(M,g)$ the first nonzero eigenvalue of the Laplace operator acting on differential forms of degree p. We prove that for $ n \geq 4$ and $ 2 \leq p \leq n - 2$, there exists a family of metrics $ {g_t}$ of volume one, such that $ {\lambda _{1,p}}(M,{g_t}) \to \infty $ as $ t \to \infty $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1277111-2
PII: S 0002-9939(1995)1277111-2
Article copyright: © Copyright 1995 American Mathematical Society