## Diff. Geom, Math. Phys., PDE Seminar: Zhifei Zhu

- Date: 04/17/2018
- Time: 15:30

University of British Columbia

I will discuss some upper bounds for the length of a shortest periodic geodesic, and the smallest area of a closed minimal surface on closed Riemannian manifolds of dimension 4 with Ricci curvature between -1 and 1. These are the first bounds that use information about the Ricci curvature rather than sectional curvature of the manifold. (Joint with Nan Wu).

I will also give examples of Riemannian metrics on the 3-disk demonstrating that the maximal area of 2-spheres arising during an "optimal" homotopy contracting its boundary cannot be majorized in terms of the volume and diameter of the 3-disc and the area of its boundary. This contrasts with earlier 2-dimensional results of Y. Liokomovich, A. Nabutovsky and R. Rotman and answers a question of P. Papasoglu. On the other hand I will show that such an upper bound exists if, instead of the volume, one is allowed to use the first homological filing function of the 3-disc. (Joint with Parker Glynn-Adey).