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A class of 3-dimensional manifolds with bounded first eigenvalue on 1-forms
Authors:Giovanni Gentile
Affiliation:Department of Mathematics, ETH-Zentrum, HG G34, CH 8092 Zurich, Switzerland
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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