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Spectrum of the Lichnerowicz Laplacian on Asymptotically Hyperbolic Surfaces

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Abstract

We show that, on any asymptotically hyperbolic surface, the essential spectrum of the Lichnerowicz Laplacian Δ L contains the ray \(\big[\frac{1}{4},+\infty\big[\). If moreover the scalar curvature is constant then − 2 and 0 are infinite dimensional eigenvalues. If, in addition, the inequality \(\langle \Delta u, u\rangle_{L^2}\geqslant \frac{1}{4}||u||^2_{L^2}\) holds for all smooth compactly supported function u, then there is no other value in the spectrum.

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  1. Laboratoire d’analyse non linéaire et géométrie, Faculté des Sciences, 33 rue Louis Pasteur, 84000, Avignon, France

    Erwann Delay

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  1. Erwann Delay
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Correspondence to Erwann Delay.

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Delay, E. Spectrum of the Lichnerowicz Laplacian on Asymptotically Hyperbolic Surfaces. Math Phys Anal Geom 11, 365–379 (2008). https://doi.org/10.1007/s11040-008-9047-6

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  • DOI: https://doi.org/10.1007/s11040-008-9047-6

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