学术报告

Degeneration of Riemannian Manifolds with Bounded Bakry-Emery Ricci Curvature

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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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