Kähler-Einstein Bergman metrics on pseudoconvex domains

Ming Xiao (UC San Diego)

Nov 21. 2023, 14:00 — 14:50

A well-known conjecture of Yau asserts that the Bergman metric on a bounded pseudoconvex domain in C^n is Kähler-Einstein if and only if the domain is homogeneous. A special case of this conjecture was posted earlier by Cheng: if the Bergman metric of a smoothly bounded strongly pseudoconvex domain is Kähler-Einstein, then the domain is biholomorphic to the unit ball. In this talk,  we will discuss old and new results concerning the conjetures of Cheng and Yau, and also explore some related questions.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Analysis and Geometry in Several Complex Variables (Workshop)
Peter Ebenfelt (UC San Diego)
Purvi Gupta (IIS Bengalore)
Bernhard Lamel (U of Vienna)
Nordine Mir (Texas A&M U at Qatar)