https://neckpinch.com/authors/robb-mcdonald/New arXiv papers by Robb McDonald, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2103.06069/arxiv:2103.06069Wed, 10 Mar 2021 00:00:00 GMTRobb McDonald — Curve shortening in the z-plane in which, at a given point on the curve, the normal velocity of the curve is equal to the curvature, is shown to satisfy SₜS_z=S_zz, where S(z,t) is the Schwarz function of the curve. This equation is shown to have a parametric solution from which the known explicit solutions for curve shortening flow; the circle, grim reaper, paperclip and hairclip, can be recovered.Curve shorteningSelf-shrinkers & translators