Curvature-free linear length bounds on geodesics in closed Riemannian surfaces
Differential Geometry
2022-10-13 v2
Abstract
This paper proves that in any closed Riemannian surface with diameter , the length of the -shortest geodesic between two given points and is at most . This bound can be tightened further to if . This improves prior estimates by A. Nabutovsky and R. Rotman.
Cite
@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}
}
Comments
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