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Bounds on harmonic radius and limits of manifolds with bounded Bakry-\'Emery Ricci curvature-张旗教授(美国加州大学河湾分校)

作者:   来源:  时间:2017-08-11

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

报告人:张旗教授(美国加州大学河湾分校)
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
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.
时间:八月11日(星期五), 4-5 PM

地点:首师大新教二楼808