4 may 2017 -- 16:00
Cortona
Abstract.
In this talk, we will present a new regularization technique of quasi-plurisubharmonic functions on a Kaehler manifold. It is a "discrete" or "localized" version of Demailly's regularization. The basic idea is to take convolutions of a plurisubharmonic function on a collection of coordinate balls first, and then we build a global object by glueing each piece together. Therefore, the advantage of this method is that the complex Hessians of the approximation functions have a better convergence behavior than previous results near the center of each ball in the collection. Moreover, all these centers form a \delta-net on the manifold eventually when the radius of the ball converges to zero.