https://neckpinch.com/authors/samuel-cuthbertson/New arXiv papers by Samuel Cuthbertson, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2411.18951/arxiv:2411.18951Thu, 28 Nov 2024 00:00:00 GMTSamuel Cuthbertson, Glen Wheeler, Valentina Wheeler — In this paper we introduce the target flow – a specific curve shortening flow with an ambient forcing term – that, given an embedded (not necessarily convex) target curve, will attempt to evolve a given source curve to that target. The motivation for this flow is to address a question of Yau. Our main result is that the target flow with uniformly normal graphical data converges smoothly to the target, broadening the class of known sources and targets such that Yau's problem has a solution.Curve shorteningOther curvature flowsLong-time existence & convergence https://neckpinch.com/papers/2411.03579/arxiv:2411.03579Wed, 06 Nov 2024 00:00:00 GMTSam Cuthbertson, Glen Wheeler, Valentina-Mira Wheeler — In this paper we consider the anisotropic curve shortening flow in the plane in the presence of an ambient force. We consider force fields in which all their derivatives are bounded in the L^(∞) sense. We prove that closed embedded curves that have a minimum of curvature sufficiently large shrink to round points. The method of proof follows along the same lines of Gage and Hamilton, in that we study a rescaling to prove curvature bounds. We additionally show that the influence of an ambient force field may make such a result untrue, by giving sufficient conditions on the ambient field that ensures eventual non-convexity of an initially convex curve evolving under the flow.Curve shortening