https://neckpinch.com/authors/michael-gene-dobbins/New arXiv papers by Michael Gene Dobbins, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2106.08907/arxiv:2106.08907Wed, 16 Jun 2021 00:00:00 GMTMichael Gene Dobbins — We study the evolution of a Jordan curve on the 2-sphere 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 Fréchet distance in the case where the curve bisects the sphere. This even holds in the limit as time goes to infinity. This builds on Joseph Lauer's work on existence and uniqueness of solutions to the curvature flow problem on the sphere when the initial curve is not smooth.Curve shorteningOther curvature flowsWeak & singular flowsStability & uniqueness