Abstract: Let $\Omega \subset \mathbb{C}^n$ be a smoothly bounded strictly pseudoconvex domain. The boundary $\partial\Omega$ is said to be obstruction flat if the log singularity (the obstruction function) of the log-potential of the complete Kähler–Einstein metric on $\Omega$ vanishes. It is called Bergman logarithmically flat if the log singularity in the Fefferman expansion of the Bergman kernel vanishes. Both notions of flatness depend only on the local CR geometry of the boundary.

In this talk, we consider real hypersurfaces arising as unit circle bundles of negative Hermitian line bundles over a complex manifold $M$. We study the relationship between obstruction flatness and Bergman logarithmic flatness of these circle bundles and the Kähler geometry of the induced metric on $M$. The talk is based on joint work with Peter Ebenfelt and Hang Xu.

Brief biography: Ming Xiao is currently a professor at the University of California, San Diego. He received his Ph.D. from Rutgers University–New Brunswick in 2015 under the supervision of Xiaojun Huang. His research focuses on several complex variables and CR geometry.

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