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A Local Existence Result for Poincaré-Einstein metrics

Published 11 Dec 2017 in math.DG | (1712.04017v1)

Abstract: Given a closed Riemannian manifold $(M, g_M)$ of dimension $n \geq 3$, we prove the existence of a conformally compact Einstein metric $g_{+}$ defined on a collar neighborhood $M \times (0,1]$ whose conformal infinity is $[g_M]$.

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