Every closed surface of genus at least 18 is Loewner

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 $g\geq 18$ satisfies Loewner's systolic ratio inequality. We also show that every clo...

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Bibliographic Details
Main Authors Li, Qiongling, Su, Weixu
Format Journal Article
LanguageEnglish
Published 01.01.2024
Subjects
Mathematics - Differential Geometry
Mathematics - Geometric Topology
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Summary: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 $g\geq 18$ satisfies Loewner's systolic ratio inequality. We also show that every closed orientable and nonpositively curved Riemannnian surface of genus $g\geq 11$ satisfies Loewner's systolic ratio inequality.
DOI:10.48550/arxiv.2401.00720