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FIELD Mathematics February 18 (Tue), 2020 16:30-18:00 1423 Yoshihiko Matsumoto Miura, Makoto CR structures, ACH-Einstein fillings, and almost complex structures 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 willpresent perturbative existence results for (I) and (II) that deform the Cheng-Yau situation. Problem (I) is a generalization of the ACHcounterpart of the Graham-Lee theorem for AHE (or Poincaré-Einstein) metrics, while (II) is completely new.

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