Einstein Metrics on Strictly Pseudoconvex Domains from the Viewpoint of Bulk-Boundary Correspondence

  • Yoshihiko Matsumoto
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 246)


We present an overview of the correspondence between asymptotically complex hyperbolic Einstein metrics and CR structures on the boundary at infinity, which is the complex version of that between Poincaré-Einstein metrics and conformal structures, with the main focus on existence results. We also propose several open problems.


Einstein equation Strictly pseudoconvex domains CR structures 



I wish to express my gratitude to the hospitality of Stanford University, where I was working as a visiting member when the manuscript was written, and I am deeply grateful to Rafe Mazzeo for hosting the visit, for discussions, and for encouragements. I would also appreciate the careful reading of the manuscript by the reviewer. This work was partially supported by JSPS KAKENHI Grant Number JP17K14189 and JSPS Overseas Research Fellowship.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceOsaka UniversityToyonaka, OsakaJapan
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

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