论文标题
在有限区域的完全刺穿球体上，最短闭合的大地测量长度的尖锐上限
Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area
论文作者
论文摘要
我们在最短的闭合大地测量球的长度上建立了尖锐的通用上限，并具有三到四个端的刺穿球体，并具有完整的Riemannian量标准有限面积。这些无曲率的上限以刺破球的面积表示。在这两种情况下，我们描述了以卡拉比 - 克罗克球体或四面体球体建模的极端指标。我们还将这些最佳不平等扩展到可逆和不必要的可逆鳍指标。在这种情况下，我们获得了具有较大穿刺的球体的最佳界限。最后，我们在最短的球/表面上，在最短的闭合大地测量长度上提出了一个大致渐近的最佳上限，该区域在该区域上具有大量穿刺。
We establish sharp universal upper bounds on the length of the shortest closed geodesic on a punctured sphere with three or four ends endowed with a complete Riemannian metric of finite area. These sharp curvature-free upper bounds are expressed in terms of the area of the punctured sphere. In both cases, we describe the extremal metrics, which are modeled on the Calabi-Croke sphere or the tetrahedral sphere. We also extend these optimal inequalities for reversible and non-necessarily reversible Finsler metrics. In this setting, we obtain optimal bounds for spheres with a larger number of punctures. Finally, we present a roughly asymptotically optimal upper bound on the length of the shortest closed geodesic for spheres/surfaces with a large number of punctures in terms of the area.
