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Seminar
FIELD Mathematics
DATE February 18 (Tue), 2020
TIME 16:30-18:00
PLACE 1423
SPEAKER Yoshihiko Matsumoto
HOST Miura, Makoto
INSTITUTE  
TITLE CR structures, ACH-Einstein fillings, and almost complex structures
ABSTRACT

I will discuss two problems on asymptotically complex hyperbolic spaces (ACH spaces): Given a domain whose boundary is equipped with a contact distribution and a “compatible” almost CR structure,
(I) construct an Einstein ACH metric whose conformal infinity is the given almost CR structure;
(II) extend the almost CR structure to an almost complex structure of the domain in a preferable way.
Our models are bounded strictly pseudoconvex domains in $\mathbb{C}^n$ equipped with Cheng-Yau’s complete Kähler-Einstein metric. I will
present perturbative existence results for (I) and (II) that deform the Cheng-Yau situation. Problem (I) is a generalization of the ACH
counterpart of the Graham-Lee theorem for AHE (or Poincaré-Einstein) metrics, while (II) is completely new.

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