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

Gentile, Giovanni

doi:10.1090/S0002-9939-99-04916-3

A class of 3-dimensional manifolds with bounded first eigenvalue on 1-forms
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by Giovanni Gentile PDF

Proc. Amer. Math. Soc. 127 (1999), 2755-2758 Request permission

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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