Journal of Spectral Theory
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Published online: 2019-03-21
Distribution of resonances for analytic asymptotically hyperbolic spacesYiran Wang (1) University of Washington, Seattle, USA
For a class of asymptotically hyperbolic metrics on the unit ball $\mathbb B^3$, we study the meromorphic properties of the resolvent of the Laplacian. In particular, we prove the existence of logarithmic type regions free of resonances (poles of the resolvent). Also, away from the region where the resonances may accumulate, we obtain a polynomial bound on the growth of the number of resonances in disks.
Keywords: Resonance, asymptotically hyperbolic manifold, analytic
Wang Yiran: Distribution of resonances for analytic asymptotically hyperbolic spaces. J. Spectr. Theory 9 (2019), 651-675. doi: 10.4171/JST/259