2025/04/29 by Christos Mantoulidis, Jared Marx-Kuo, Mantoulidis, Christos +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.2504.20895
In this note we use classical tools from min-max and hyperbolic geometry to substantiate a folklore example in Almgren--Pitts min-max theory, the three-legged starfish metric on a 2-sphere, whose systolic length, Almgren--Pitts width, and Gromov--Guth width are attained by ``figure-eight'' geodesics. We also recover a hyperbolic geometry fact about ``figure-eight'' geodesics using min-max.