题目：Degeneration of Riemannian Manifolds with Bounded Bakry-Emery Ricci Curvature

报告人： 朱萌 研究员 (华东师范大学)

地点：致远楼101室

时间：2019年10月26日14：30-15：30

Abstract:

We study the regularity of the Gromov-Hausdorff limits of Riemannian manifolds with bounded Bakry-Emery Ricci curvature, which include the Ricci soliton and bounded Ricci curvature cases. Our main results are the generalizations of the works of Cheeger-Colding-Tian-Naber when the manifolds are volume noncollapsed. The new ingredients here are a Bishop-Gromov type relative volume comparison theorem on the original manifold without involving weight, and proving that the C/α harmonic radius can be bounded from below, which has relaxed 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.

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