2025/03/19 by Vanderson Lima, Lima, Vanderson
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2503.14846
openalex publication_date 2025/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On a closed Riemannian surface of negative curvature, we prove a characterization for configurations of closed geodesics arising from one parameter Allen-Cahn min-max constructions. One of the facts we conclude is that every geodesic occurs with multiplicity one. As an application we obtain a uniform sharp lower bound for the first min-max width of closed hyperbolic surfaces and prove it is only attained asymptotically. Moreover, we compute the first width of the Bolza surface and of some hyperbolic surfaces with small systoles.