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Degeneration of manifolds with bounded Bakry-Emery Ricci curvature
时间  Datetime
2017-12-11 13:00 — 14:00 
地点  Venue
1106, Math Building
报告人  Speaker
朱萌
单位  Affiliation
华东师范大学
邀请人  Host
来米加
报告摘要  Abstract

In this talk, we study the regularity of the Gromov-Hausdorff limits of Riemannian manifolds with bounded Bakry-Emery Ricci curvature, which includes the Ricci soliton and bounded Ricci curvature cases.
We generalize Cheeger-Colding-Tian-Naber's results when the manifolds are volume noncollapsing.  Our new ingredient here are a Bishop-Gromov type relative volume comparison theorem on the original manifold without involving weight, and proving that  the C^{\alpha} harmonic radius can be bounded from below, which has weakened Anderson's result. Our proof of the Codimension 4 Theorem essentially follows the guideline of Cheeger-Naber, but we managed to shorten the proof by using Green's function and a linear algebra argument of R. Bamler. These are joint works with Qi S. Zhang.