2024/01/01 by Qiongling Li, Li, Qiongling, Weixu Su +1
Mathematics · #Analytic and geometric function theory #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2401.00720
In this paper, we obtain an improved upper bound involving the systole and area for the volume entropy of a Riemannian surface. As a result, we show that every orientable and closed Riemannian surface of genus g≥ 18 satisfies Loewner's systolic ratio inequality. We also show that every closed orientable and nonpositively curved Riemannnian surface of genus g≥ 11 satisfies Loewner's systolic ratio inequality.