Kähler-Einstein metrics on complex hyperbolic cusps

Geometric Analysis and Application
Event time: 
Friday, May 6, 2022 - 2:00pm
Hans-Joachim Hein
Speaker affiliation: 
University of Munster
Event description: 


A complex hyperbolic cusp is an end of a finite-volume quotient of complex hyperbolic space. Up to a finite cover, any such cusp can be realized as the punctured unit disk bundle of a negative line bundle over an abelian variety. The Dirichlet problem for complete Kähler-Einstein metrics on this space with boundary data prescribed on the unit circle bundle is well-posed. We determine the precise asymptotics of its solutions towards the zero section. Time permitting I will also mention an application to gluing constructions for Kähler-Einstein metrics on surfaces of general type. This is joint work with Xin Fu and Xumin Jiang.