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.