SEMINARS
Degeneration of manifolds with bounded Bakry-Emery Ricci curvature

2017-12-11　13:00 — 14:00

1106, Math Building

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.