TY - JOUR
T1 - Poincaré-Lovelock metrics on conformally compact manifolds
AU - Albin, Pierre
N1 - Publisher Copyright:
© 2020
PY - 2020/6/24
Y1 - 2020/6/24
N2 - 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.
AB - 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.
KW - Asymptotically hyperbolic
KW - Conformally compact
KW - Lovelock
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U2 - 10.1016/j.aim.2020.107108
DO - 10.1016/j.aim.2020.107108
M3 - Article
AN - SCOPUS:85081684781
SN - 0001-8708
VL - 367
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 107108
ER -