Poincare-Lovelock metrics on conformally compact manifolds
Differential Geometry
2019-01-09 v1
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.
Keywords
Cite
@article{arxiv.1901.02344,
title = {Poincare-Lovelock metrics on conformally compact manifolds},
author = {Pierre Albin},
journal= {arXiv preprint arXiv:1901.02344},
year = {2019}
}