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

TL;DR

This paper establishes a polynomial upper bound on the number of resonances for certain hyperbolic manifolds and Schwarzschild-de Sitter spacetimes, advancing understanding of their spectral properties.

Contribution

It provides the first polynomial upper bound on resonances for even asymptotically hyperbolic manifolds with real-analytic ends and extends this to quasinormal frequencies in Schwarzschild-de Sitter spacetimes.

Findings

Polynomial upper bound on resonances for hyperbolic manifolds

Similar bound on quasinormal frequencies in Schwarzschild-de Sitter spacetimes

Enhanced understanding of spectral distribution in these geometries

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.