Monotonicity of the modulus under curve shortening flow
Differential Geometry
2026-04-15 v2 Analysis of PDEs
Abstract
Given two disjoint nested embedded closed curves in the plane, both evolving under curve shortening flow, we show that the modulus of the enclosed annulus is monotonically increasing in time. An analogous result holds within any ambient surface satisfying a lower curvature bound.
Cite
@article{arxiv.2409.03098,
title = {Monotonicity of the modulus under curve shortening flow},
author = {Arjun Sobnack and Peter M. Topping},
journal= {arXiv preprint arXiv:2409.03098},
year = {2026}
}