闭黎曼曲面上测地线的无曲率线性长度界
微分几何
2022-10-13 v2
摘要
本文证明了在任意直径为 的闭黎曼曲面 中，给定两点 与 之间第 短测地线的长度至多为 。若 ，此界可进一步收紧至 。这改进了 A. Nabutovsky 与 R. Rotman 先前的估计。
引用
@article{arxiv.2109.00438,
title = {Curvature-free linear length bounds on geodesics in closed Riemannian surfaces},
author = {Herng Yi Cheng},
journal= {arXiv preprint arXiv:2109.00438},
year = {2022}
}
备注
21 pages, 7 figures. To be published in Tran. Amer. Math. Soc. Minor revisions only, such as: main result restricted to the main case of 2-spheres while valid for other closed surfaces; minor corrections to the statements of Lemmas 3.3, 3.4 and 4.1, and to the labeling of Figure 6; hand-drawn figures replaced with vector graphics; cap product structure uses c in H^2, not H^1