Sharp distance comparison for curve shortening flow on the round sphere
Differential Geometry
2023-10-05 v1
Abstract
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).
Keywords
Cite
@article{arxiv.2310.02649,
title = {Sharp distance comparison for curve shortening flow on the round sphere},
author = {Paul Bryan and Mat Langford and Jonathan J. Zhu},
journal= {arXiv preprint arXiv:2310.02649},
year = {2023}
}