Delayed parabolic regularity for curve shortening flow
Analysis of PDEs
2025-09-17 v2 Differential Geometry
Abstract
Given two curves bounding a region of area that evolve under curve shortening flow, we propose the principle that the regularity of one should be controllable in terms of the regularity of the other, starting from time . We prove several results of this form and demonstrate that no estimate can hold before that time. As an example application, we construct solutions to graphical curve shortening flow starting with initial data that is merely an function.
Cite
@article{arxiv.2408.04049,
title = {Delayed parabolic regularity for curve shortening flow},
author = {Arjun Sobnack and Peter M. Topping},
journal= {arXiv preprint arXiv:2408.04049},
year = {2025}
}
Comments
v1 was not submitted. v2 has numerous adjustments and improvements to the exposition