Asymptotics of ACH-Einstein Metrics

作者：Matsumoto Yoshihiko^*

来源：Journal of Geometric Analysis, 2014, 24(4): 2135-2185.

DOI：10.1007/s12220-013-9411-z

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

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.

• 出版日期2014-10