English

The continuity of curvature flow in Fr\'echet distance

Differential Geometry 2023-12-27 v1 Analysis of PDEs Metric Geometry

Abstract

We study the evolution of a Jordan curve on the plane by curvature flow, also known as curve shortening flow, and by level-set flow, which is a weak formulation of curvature flow. We show that the evolution of the curve depends continuously on the initial curve in Fr\'echet distance.

Keywords

Cite

@article{arxiv.2312.15005,
  title  = {The continuity of curvature flow in Fr\'echet distance},
  author = {Shiyi Ma},
  journal= {arXiv preprint arXiv:2312.15005},
  year   = {2023}
}

Comments

11 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2106.08907 by other authors