Poincaré-Lovelock metrics on conformally compact manifolds

Research output: Contribution to journalArticle

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, Poincaré-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.

Original languageEnglish (US)
Article number107108
JournalAdvances in Mathematics
Volume367
DOIs
StatePublished - Jun 24 2020

Keywords

  • Asymptotically hyperbolic
  • Conformally compact
  • Lovelock

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Poincaré-Lovelock metrics on conformally compact manifolds'. Together they form a unique fingerprint.

  • Cite this