Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	陈张驰，南巴黎大学
Inviter:
Title:	Unique ergodicity for foliations of compact K?hler surfaces
Time & Venue:	2019.4.23 9:30-11:30 N820
Abstract:	The study of foliation arises from Hilberts 16th problem and PDE systems. The theory links among dynamic systems, lie group actions and complex analysis. In this talk we study a foliations F of a compact K?hler surface by Rieman surfaces, and we suppose all the singularities of F are hyperbolic. To study the distribution of the leaves, we can analyse a directed positive ddc- closed current. The unique ergodicity states that if F admits no directed positive closed current, then there exists a unique positive ddc-closed current T of mass 1. The case of P2 is proved in 2006 by Fornaess and Sibony, with heavy calculations on geometric intersections. In 2018 Dihn, Nguyen and Sibony proved the case of compact K?hler surfaces, by studying the density of a tensor product of foliations.