“From curve shortening to flat link stability and Birkhoff sections of geodesic flows”
Martedì 3 Dicembre 2024, ore 14:30 - Aula 2BC30 - Marco Mazzucchelli (ENS Lyon)
Abstract
In this talk, based on joint work with Marcelo Alves, I will present three new theorems on the dynamics of geodesic flows of closed Riemannian surfaces, proved using the curve shortening flow.
The first result is the stability, under $C^0$-small perturbations of the Riemannian metric, of certain flat links of closed geodesics. The second one is a forced existence theorem for closed geodesics on orientable closed Riemannian surfaces. The third theorem asserts the existence of Birkhoff sections for the geodesic flow of any closed orientable Riemannian surface.
