Every closed surface of genus at least 18 is Loewner
Differential Geometry
2024-01-10 v2 Geometric Topology
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 satisfies Loewner's systolic ratio inequality. We also show that every closed orientable and nonpositively curved Riemannnian surface of genus satisfies Loewner's systolic ratio inequality.
Cite
@article{arxiv.2401.00720,
title = {Every closed surface of genus at least 18 is Loewner},
author = {Qiongling Li and Weixu Su},
journal= {arXiv preprint arXiv:2401.00720},
year = {2024}
}
Comments
11 pages, 1 figures. We correct an erroneous citation in previous the version