Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary

Isabel Beach

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arXiv · 2507.07797

Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary

Isabel Beach

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Abstract

We prove the existence of at least two distinct short, simple orthogonal geodesic chords on a Riemannian 2-disk $M$ with convex boundary. The lengths of these curves are bounded in terms of the length of $\partial M$, the diameter of $M$, and the area of $M$. We also prove the existence of a short, simple geodesic chord on any Riemannian 2-disk.

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Isabel Beach. 2025-07-10. Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary. https://arxiv.org/abs/2507.07797

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