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# Nan Wu : Length of a shortest closed geodesic in manifolds of dimension 4

In this talk, we show that for any closed 4-dimensional simply-connected Riemannian manifold $M$ with Ricci curvature $|Ric| \leq 3$, volume $vol(M)>v>0$ and diameter $diam(M) \leq D$, the length of a shortest closed geodesic on $M$ is bounded by a function $F(v,D)$ . The proof of this result is based on the diffeomorphism finiteness theorem for the manifolds satisfying above conditions proved by J. Cheeger and A. Naber. This talk is based on the joint work with Zhifei Zhu.

**Category**: Geometry and Topology**Duration**: 01:24:40**Date**: January 22, 2018 at 3:10 PM**Views**: 102-
**Tags:**seminar, Geometry/topology Seminar

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