TY - UNPB
T1 - Sharp distance comparison for curve shortening flow on the round sphere
AU - Bryan, Paul
AU - Langford, Mat
AU - Zhu, Jonathan J.
PY - 2023/10/4
Y1 - 2023/10/4
N2 - 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).
AB - 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).
U2 - 10.48550/arXiv.2310.02649
DO - 10.48550/arXiv.2310.02649
M3 - Preprint
T3 - arXiv
BT - Sharp distance comparison for curve shortening flow on the round sphere
PB - arXiv.org
ER -