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

  • Date: 04/17/2018
  • Time: 15:30
Zhifei Zhu, University of Toronto

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).

Other Information: 

Location: ESB 2012