Geometry Seminar: Z. Zhu (YMSC, Tsinghua U.)

Geometry Seminar (Geometric Analysis)

Speaker: Zhifei Zhu (YMSC, Tsinghua U.)

Title: Systolic inequality on Riemannian manifold with bounded Ricci curvature

Abstract: In this talk, we show that the length of a shortest closed geodesic on a Riemannian manifold of dimension 4 with diameter D, volume v, and |Ric|<3 can be bounded by a function of v and D. In particular, this function can be explicitly computed if the manifold is Einstein. The proof of this result depends on a structural theorem proven by J. Cheeger and A. Naber. This is joint work with N. Wu.