2018年度suncitygroup太阳新城外请专家学术报告之二十五
时间：2018-07-07 13:32:59 来源：suncitygroup太阳新城 作者： 阅读： 次
报告题目1： On the CR Gradient Estimate
报告人： 张树城 教授（台湾大学）
报告时间： 2018年7月12日（周四）8:00—10:00
报告地点： suncitygroup太阳新城学术报告厅
报告摘要: In the seminal paper of P. Li and S.-T. Yau, they established the well known gradient estimates for the positive solutions to the heat equation on the complete Riemannian manifolds, since then it becomes a powerful tool in differential geometry, PDE, etc. In this talk, with the help of CR Bochner formula, we are able to have the Li-Yau gradient estimate for the CR heat equation in a closed pseudohermitian manifold of vanishing torsion. Furthermore, with the help of a generalized curvature-dimension inequality, we are able to obtain such a CR gradient estimate in case of non-vanishing torsion tensor. Finally, I will discuss some possible applications, in particular, the Hamilton Harnack quantity for the CR torsion flow.
报告题目2： On the Classification of CR Torsion Solitons
报告人： 张树城 教授（台湾大学）
报告时间： 2018年7月12日（周四）10:00—12:00
报告地点： suncitygroup太阳新城学术报告厅
报告摘要: In this talk, we investigate the geometry and classification of closed three dimensional CR torsion solitons . We derive the CR Harnack quantity and obtain a classification theorem of three-dimensional CR torsion solitons of negative or positive pseudohermitian curvature. In addition, we obtain the obstruction theorem in a three-dimensional CR manifold of positive pseudohermitian curvature.
报告人简介：张树城，博士，教授，博士生导师，杰出的几何分析学家。1985-1990在莱斯大学学习并获博士学位，2004-2007年间任台湾清华大学数学系系主任，2008年至今任教于国立台湾大学。主要研究领域为：微分几何、几何分析、伪Hermitian几何、Kaehler几何等。近年来专注于CR流形中的几何分析问题，包括CR Obata问题、CR heat equation 相应的Li-Yau gradient estimate，linear trace Li-Yau-Hamilton inequality问题的研究。在国际著名学术期刊，如J. Differential Geometry、Math Ann.、J. Geometric Analysis、Trans. AMS 等发表系列重要研究成果。
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