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arXiv · 2401.00720

Every closed surface of genus at least 18 is Loewner

Qiongling Li·Weixu Su
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Abstract

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.

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Qiongling Li, Weixu Su. 2024-01-09. Every closed surface of genus at least 18 is Loewner. https://arxiv.org/abs/2401.00720

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