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(7月10日)张旗教授:Bounds on harmonic radius and limits of manifolds with bounded Bakry-\'Emery Ricci curvature
来源: 陈黎   发布时间:2017-6-30   阅读次数:608

报告人:Professor Qi Zhang(University of California, Riverside; 复旦大学
时间:2017年7月10日(星期一下午)14:30-15:30
地点:浙大玉泉校区工商楼200-9报告厅

Title: Bounds on harmonic radius and  limits of manifolds with bounded
Bakry-\'Emery Ricci curvature

Abstract: 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
by Anderson. This loss of regularity induces difference in the proof.

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.

联系人: 盛为民教授(shengweimin@zju.edu.cn

 

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