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Bounds on harmonic radius and limits of manifolds with bounded Bakry-\'Emery Ricci curvature
发布时间: 2017-06-19     13:34   【返回上一页】 发布人:张旗


 北京师范大学数学科学学院

 

周五公众报告

 

 

 

 

报告题目:Bounds on harmonic radius and  limits of manifolds with bounded Bakry-/'Emery Ricci curvature

 

 

报告人: 张旗 教授

 

(UC Riverside 复旦大学)

 

 

时间地点:2017623日下午13:45-14:45, 后主楼1220

 

 

邀请人:黄红

 

 

报告摘要:Under the usual condition that the volume of a geodesic ball is close to the Euclidean one, we prove a lower bound of the $C^{/alpha} /cap  W^{1,q }$  harmonic radius for manifolds with bounded Bakry-/'Emery Ricci curvature when the gradient of the potential is bounded. This is almost 1 order lower than that in the classical $C^{1,/a} /cap W^{2, p}$ harmonic coordinates under bounded Ricci curvature condition  /cite{And}. The method of proof can also be used to  address the  detail of $W^{2, p}$ convergence in the classical case, which seems  not in the literature.

       Based on this lower bound and the techniques in Cheeger and Naber and F. Wang and X.H. Zhu, we extend Cheeger-Naber's Codimension 4 Theorem  to the case where the manifolds have  bounded Bakry-/'Emery Ricci curvature when the gradient of the  potential is bounded.  This result covers Ricci solitons when the gradient of the potential is bounded. Some short cuts and additional information in the original case are  also obtained.

      This is joint work with Zhu Meng.

 

报告人简介:张旗(Qi S. Zhang)  是美国UC Riverside(加州大学河滨分校)和中国复旦大学教授。他在偏微分方程(包括Navier-Stokes方程组)和几何分析(包括Ricci流)领域有很多出色的工作, 已发表论文80余篇。 他2011年在美国CRC出版社出版的书《Sobolev inequalities, heat kernels under Ricci flow, and the Poincaré conjecture》的中译本已由北京大学出版社于2013年出版。

 

 

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