Upper bound on the number of resonances for even asymptotically hyperbolic manifolds with real-analytic ends

Abstract

We prove a polynomial upper bound on the number of resonances in a disc whose radius tends to infinity for even asymptotically hyperbolic manifolds with real-analytic ends. Our analysis also gives a similar upper bound on the number of quasinormal frequencies for Schwarzschild-de Sitter spacetimes.

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