W. Jacob Ogden — Neckpinchhttps://neckpinch.com/authors/w-jacob-ogden/New arXiv papers by W. Jacob Ogden, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Grim Raindrop: A Translating Solution to Curve Diffusion Flowhttps://neckpinch.com/papers/2412.15934/arxiv:2412.15934Fri, 20 Dec 2024 00:00:00 GMTW. Jacob Ogden, Micah Warren — We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, namely ( dX/dt) ^(⊥)=−κₛₛN.Curve shorteningSelf-shrinkers & translators