English

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}
}