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Mathematical Physics, Analysis and Geometry

, Volume 11, Issue 3–4, pp 365–379 | Cite as

Spectrum of the Lichnerowicz Laplacian on Asymptotically Hyperbolic Surfaces

  • Erwann Delay
Article

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.

Keywords

Asymptotically hyperbolic surfaces Lichnerowicz Laplacian Symmetric 2-tensor Essential spectrum Asymptotic behavior 

Mathematics Subject Classifications (2000)

35P15 58J50 47A53 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Laboratoire d’analyse non linéaire et géométrie, Faculté des SciencesAvignonFrance

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