In this talk, I will survey the recent progress toward the CR analogue of Yau's uniformization conjectures in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e. Sasakian manifold) which is an odd dimensional counterpart of Kaehler geometry. Finally, we mainly focus with the problem of the sharp dimension estimate of CR holomorphic functions.

简介：張樹城教授是一位幾何分析學家。近來張教授專注於研究CR流形中的幾何分析問題，包括 CR Obata 問題、CR heat equation 相應的 Li-Yau gradient estimate, Li-Yau-Hamilton inequality, CR Yau's uniformization conjecture 等，更是將他的研究推向另一個高峰。其文章發表在包括 JDG, Math. Ann. , Indiana Univ. Math. J. , Trans.  AMS,  JGEA 等傑出期刊。並因此榮獲2015年台湾數學會學術獎殊榮。

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