A distance comparison principle for curve shortening flow with free boundary
Differential Geometry
2023-09-22 v2
Abstract
We introduce a reflected chord-arc profile for curves with orthogonal boundary condition and obtain a chord-arc estimate for embedded free boundary curve shortening flows in a convex planar domain. As a consequence, we are able to prove that any such flow either converges in infinite time to a (unique) ``critical chord'', or contracts in finite time to a ``round half-point'' on the boundary.
Keywords
Cite
@article{arxiv.2302.14258,
title = {A distance comparison principle for curve shortening flow with free boundary},
author = {Mat Langford and Jonathan J. Zhu},
journal= {arXiv preprint arXiv:2302.14258},
year = {2023}
}
Comments
32 pages, 2 figures; adjusted to a more precise barrier function in Theorem 5.3