A Local Existence Result for Poincaré-Einstein metrics

2017/12/11 by Gursky, Matthew J., Székelyhidi, Gábor · 2 citations
#53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.04017

Abstract

Given a closed Riemannian manifold (M, g_M) of dimension n ≥ 3, we prove the existence of a conformally compact Einstein metric g₊ defined on a collar neighborhood M × (0,1] whose conformal infinity is [g_M].

Cited by

• Conformal characterization of the Fefferman-Graham ambient metric
• Poincaré-Einstein 4-manifolds with conformally Kähler geometry

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• Topics in conformally compact Einstein metrics
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