Absence of Resonances near Critical Line for CC Manifolds

TL;DR

This paper establishes a polynomially close resonance-free region near the critical line for conformally compact manifolds with polyhomogeneous metrics, advancing understanding of spectral properties in geometric analysis.

Contribution

It proves the existence of a resonance-free region near the critical line for a class of manifolds, which was previously unknown.

Findings

Resonance-free region established near the critical line

Polyhomogeneous metrics allow for polynomial proximity to the critical line

Advances spectral analysis on conformally compact manifolds

Abstract

We find a resonance free region polynomially close to the critical line on Conformally compact manifolds with polyhomogeneous metric.