# Calendar

Topology/Geometry Seminar

## Ricci flow on manifolds with bounded Ricci curvature and almost maximal local rewinding volume

Location:  Hill 525
Date & time: Tuesday, 27 September 2016 at 3:30PM - 3:31PM

Lina Chen, Capital Normal University, China: Motivated by studying the quantitative volume space form rigidity conjecture: a closed $$n$$-manifold $$M$$ with lower Ricci curvature bounded by $$(n-1)H$$ and almost maximal local rewinding volume is diffeomorphic to a $$H$$-space form. In this paper, we consider $$M$$ with additional Ricci curvature upper bound by using Ricci flow method. We will show that the Ricci flow on $$M$$ exists for a definite time and the $$L_p$$ norm of the Ricci tensor is preserved by the flow. Using these results we have that $$M$$ admits a metric with almost $$H$$-constant section curvature. And together with our earlier work in [CRX] , we prove that the above rigidity conjecture holds under additional Ricci curvature upper bound. Some ideas of the proofs come from [DWY].

And it is a joint work with professor Xiaochun Rong and Shicheng Xu.

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