亏格至少为18的每个闭曲面是Loewner的
Every closed surface of genus at least 18 is Loewner
AI总结：
本文改进了Riemannian曲面体积熵的上界，证明了亏格至少为18的可定向闭曲面及亏格至少为11的非正曲率闭曲面均满足Loewner的systolic比不等式。
摘要：
本文获得了涉及Riemannian曲面体积熵的systole和面积的改进上界。由此，我们证明了亏格$g\geq 18$的每个可定向闭Riemannian曲面满足Loewner的systolic比不等式。我们还证明了亏格$g\geq 11$的每个闭可定向且非正曲率Riemannian曲面满足Loewner的systolic比不等式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
