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arXiv · 0802.3174

Spectrum of the Lichnerowicz Laplacian on asymptotically hyperbolic surfaces

Erwann Delay
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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 $[{1/4},+\infty[$. If moreover the scalar curvature is constant then -2 and 0 are infinite dimensional eigenvalues. If, in addition, the inequality $<Δu, u>_{L^2}\geq \frac14||u||^2_{L^2}$ holds for all smooth compactly supported function $u$, then there is no other value in the spectrum.

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Erwann Delay. 2008-02-21. Spectrum of the Lichnerowicz Laplacian on asymptotically hyperbolic surfaces. https://doi.org/10.1007/s11040-008-9047-6

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