Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends

TL;DR

This paper investigates the spectral properties of asymptotically hyperbolic manifolds with warped-product ends, providing an upper bound on the resonance counting function based on geometric constants related to the manifold's core and ends.

Contribution

It introduces a new upper bound on resonance counting functions for this class of manifolds, linking spectral asymptotics with geometric Weyl constants.

Findings

Derived an explicit upper bound for resonance counting functions

Connected resonance asymptotics with geometric Weyl constants

Enhanced understanding of spectral theory for warped-product ends

Abstract

We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped product type. Our main result is an upper bound on the resonance counting function with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base manifold defining the ends.