# Poincare-Lovelock metrics on conformally compact manifolds

## TL;DR

This paper extends the Fefferman-Graham expansion to Poincare-Lovelock metrics, a generalization of Einstein metrics, and demonstrates their existence near the round sphere conformal class.

## Contribution

It proves that Poincare-Lovelock metrics admit Fefferman-Graham expansions and establishes existence of such metrics filling the ball near the round sphere.

## Key findings

- Fefferman-Graham expansions exist for Poincare-Lovelock metrics
- Existence of fillings satisfying Lovelock equations near the round sphere
- Extension of Graham-Lee's Einstein metric results to Lovelock metrics

## Abstract

An important tool in the study of conformal geometry, and the AdS/CFT correspondence in physics, is the Fefferman-Graham expansion of conformally compact Einstein metrics. We show that conformally compact metrics satisfying a generalization of the Einstein equation, Poincare-Lovelock metrics, also have Fefferman-Graham expansions. Moreover we show that conformal classes of metrics that are near that of the round metric on the n-sphere have fillings into the ball satisfying the Lovelock equation, extending the existence result of Graham-Lee for Einstein metrics.