DG-MP-PDE Seminar: Closed geodesics and Alexandrov spaces

In this talk we will present our recent work on ‘’Closed geodesics in Alexandrov spaces of curvature bounded from above’’. This is an extension of Colding and Minicozzi’s width-sweepout construction of closed geodesics on closed Riemannian manifold to the Alexandrov setting, which provides a generalized version of the Birkhoff-Lyusternik theorem on the existence of non-trivial closed geodesics. We will explain how the width-sweepout construction works and discuss some future work in this direction.