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In this talk, we will focus on the CR analogue of Yau's uniformization conjecture in a complete noncompact pseudohermitian (2n+1)-manifold of vanishing torsion (i.e. Sasakian manifold) which is an odd dimensional counterpart of Kähler geometry. And we obtain the sharp dimension estimate of CR holomorphic functions in a complete noncompact pseudohermitian manifold of vanishing torsion with nonnegative pseudohermitian bisectional curvature.

2019年11月8日10:00-11:00 摘要：A compact polyhedron $X$ is said to have the /emph{Bounded Index Property (BIP)} if there is an integer $/B>0$ such that for any map $f: X/rightarrow X$ and any fixed point class

Clustering of extremes usually has a large societal impact. The extremal index, a number in the unit interval, is a key parameter in modelling the clustering of extremes.

In this talk, I will present some recent results on the compactness of the solutions to the Yamabe problem on manifolds with boundary. The compactness of Yamabe problem was introduced by Schoen in 1988. There have been a lot of works on this topic later on. This is a joint work with Sergio Almaraz and Olivaine Queiroz.

In this talk, we will present two formulas on scalar curvatures of canonical Hermitian connections on an almost Hermitian manifold. Then we will show some inequalities of various total scalar curvatures and some characterization results. Finally, we will talk about some applications. This is a joint work with Jixiang Fu.