Scattering theory and deformations of asymptotically hyperbolic metrics

TL;DR

This paper investigates how the resolvent and scattering operators depend continuously on asymptotically hyperbolic metrics, providing insights into their stability under metric deformations.

Contribution

It establishes the continuity of resolvent and scattering operators with respect to metric changes in the setting of asymptotically hyperbolic manifolds.

Findings

Resolvent operator varies continuously with the metric.

Scattering operator depends continuously on metric deformations.

Provides a framework for analyzing metric stability in hyperbolic geometry.

Abstract

For an asymptotically hyperbolic metric on the interior of a compact manifold with boundary, we prove that the resolvent and scattering operators are continuous functions of the metric in the appropriate topologies.