Length of a shortest closed geodesic in manifolds of dimension 4

Geometry/topology Seminar

Nan Wu (University of Toronto)

Monday, January 22, 2018 -
3:15pm to 4:15pm
119 Physics

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.

Last updated: 2017/12/17 - 4:21am