Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary
Differential Geometry
2025-07-11 v1
Abstract
We prove the existence of at least two distinct short, simple orthogonal geodesic chords on a Riemannian 2-disk with convex boundary. The lengths of these curves are bounded in terms of the length of , the diameter of , and the area of . We also prove the existence of a short, simple geodesic chord on any Riemannian 2-disk.
Keywords
Cite
@article{arxiv.2507.07797,
title = {Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary},
author = {Isabel Beach},
journal= {arXiv preprint arXiv:2507.07797},
year = {2025}
}
Comments
17 pages, 6 figures