The Journal of Geometric Analysis

, Volume 24, Issue 4, pp 2135–2185 | Cite as

Asymptotics of ACH-Einstein Metrics



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.


ACH metrics The Einstein equation Partially integrable almost CR manifolds The CR obstruction tensor 

Mathematics Subject Classification

32V05 53A55 


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© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

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