Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Lima, Vanderson
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414901995
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