Ricci flow of conformally compact metrics

TL;DR

This paper proves short-time existence of Ricci flow for conformally compact metrics and establishes stability results for conformally compact Einstein metrics near hyperbolic space.

Contribution

It introduces a method to evolve conformally compact metrics under Ricci flow and demonstrates stability of Einstein metrics close to hyperbolic space.

Findings

Existence of short-time Ricci flow solutions for conformally compact metrics.

Stability of conformally compact Einstein metrics near hyperbolic space.

Adaptation of recent mathematical results to this setting.

Abstract

In this paper we prove that given a smoothly conformally compact metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact. We adapt recent results of Schn\"urer, Schulze and Simon to prove a stability result for conformally compact Einstein metrics sufficiently close to the hyperbolic metric.