非正曲面是 Loewner

The Journal of Geometric Analysis Pub Date : 2024-07-10 DOI:10.1007/s12220-024-01732-4

Mikhail G. Katz, Stéphane Sabourau

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引用次数: 0

摘要

我们证明了每一个封闭的非正曲曲面都满足卢弗纳的收缩不等式。证明依赖于高斯-波内特公式与利用大地流下柳维尔量不变性的平均论证的结合。这使我们能够找到一个在其中心周围具有较大总曲率的圆盘，从而产生较大的面积。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Nonpositively Curved Surfaces are Loewner

We show that every closed nonpositively curved surface satisfies Loewner’s systolic inequality. The proof relies on a combination of the Gauss–Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic flow. This enables us to find a disk with large total curvature around its center yielding a large area.

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The Journal of Geometric Analysis

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