https://neckpinch.com/authors/paul-bryan/New arXiv papers by Paul Bryan, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2310.02649arxiv:2310.02649Wed, 04 Oct 2023 00:00:00 GMTPaul Bryan, Mat Langford, Jonathan J. Zhu — We prove that curve shortening flow on the round sphere displays sharp chord-arc improvement, precisely as in the planar setting (Andrews and Bryan, Comm. Anal. Geom., 2011). As in the planar case, the sharp estimate implies control on the curvature, resulting in a direct and efficient proof that simple spherical curves either contract to round points (in finite time) or converge to great circles (in infinite time).Curve shorteningSingularities