On the CR Gradient Estimate
报 告 人:: 张树城
报告地点:: 数学与统计学院104室
报告时间:: 2018年04月20日星期五14:00-15:00

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.

发 布 人:吴双 发布时间: 2018-04-16
张树城,台湾大学教授,是幾何分析學家,曾獲2015年數學會學術獎,在科學委員會擔任審議及諮詢委員多年,2006起連續獲得多年期研究計畫資助。其關於external metric相關性質的早期研究成果發表在Math. Ann. 2002及Indiana Univ. Math. J. 2004等;在幾何流,包括Calabi flow, Yamabe flow, Ricci flow, Q-curvature flow等高階非線性方程方面發表了一系列關於這些幾何流存在性、收斂性及相關性質的文章,如:Math. Ann. 2000及Indiana Univ. Math. J. 2007等;近來專注於研究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, linear trace Li-Yau-Hamilton inequality等,將他的研究推向另一個高峰,從2009迄今共有25篇,包括2篇JDG,2篇Math. Ann.,3篇Trans. AMS,4篇J. Geom. Anal.,1篇Indiana Univ. Math. J. 和1篇CAG 等傑出期刊文章。