Mathematics – Differential Geometry
Scientific paper
2008-02-21
Mathematics
Differential Geometry
13 pages
Scientific paper
10.1007/s11040-008-9047-6
We show that, on any asymptotically hyperbolic surface, the essential spectrum of the Lichnerowicz Laplacian $\Delta_L$ 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 $<\Delta u, u>_{L^2}\geq \frac14||u||^2_{L^2}$ holds for all smooth compactly supported function $u$, then there is no other value in the spectrum.
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