Poincaré-Lovelock metrics on conformally compact manifolds

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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
StatePublished - Jun 24 2020


  • Asymptotically hyperbolic
  • Conformally compact
  • Lovelock

ASJC Scopus subject areas

  • General Mathematics


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