Asymptotics of ACH-Einstein metrics

2010/09/21 by Yoshihiko Matsumoto, Y. Matsumoto, Matsumoto, Yoshihiko
Mathematics · Physics and Astronomy · #32V05 (Primary) #53A55 (Secondary) #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:32V05 #msc:53A55

paper · pdf · doi:10.48550/arxiv.1009.4163

44 pages; introduction rewritten, proof of Proposition 1.4 fixed, minor modifications added

openalex publication_date 2010/09/21 · arxiv created 2011/02/28 · arxiv updated 2011/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundary asymptotics of ACH metrics which are formally Einstein. In terms of the partially integrable almost CR structure induced on the boundary at infinity, existence and uniqueness of such formal asymptotic expansions are studied. It is shown that there always exist formal solutions to the Einstein equation if we allow logarithmic terms, and that a local CR-invariant tensor arises as the obstruction to the existence of a log-free solution. Some properties of this new CR invariant, the CR obstruction tensor, are discussed.

Citations

• The Ambient Obstruction Tensor and Q-Curvature
• On the existence of a complete Kähler metric on non‐compact complex manifolds and the regularity of fefferman's equation

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