https://neckpinch.com/authors/gonzalo-contreras/New arXiv papers by Gonzalo Contreras, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2204.11977/arxiv:2204.11977Mon, 25 Apr 2022 00:00:00 GMTGonzalo Contreras, Gerhard Knieper, Marco Mazzucchelli, Benjamin H. Schulz — We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section Σ that we construct are either Birkhoff sections, meaning that they intersect every sufficiently long orbit segment of the geodesic flow, or at least they have some hyperbolic components in ∂Σ as limit sets of the orbits of the geodesic flow that do not return to Σ. In order to prove these theorems, we provide a study of configurations of simple closed geodesics of closed orientable Riemannian surfaces, which may have independent interest. Our arguments are based on the curve shortening flow.Curve shortening