https://neckpinch.com/authors/nathan-burns/New arXiv papers by Nathan Burns, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.12817arxiv:2610.12817Thu, 08 Oct 2026 00:00:00 GMTTheodora Bourni, Nathan Burns, Marcus Flook — We construct compact, embedded solutions to the mean curvature flow in ℝⁿ⁺¹ that arise from various non-compact initial data and exist for a finite time.Mean curvature flowSingularitiesBoundaries & non-compact https://arxiv.org/abs/2603.06949arxiv:2603.06949Fri, 06 Mar 2026 00:00:00 GMTTheodora Bourni, Nathan Burns, Mat Langford — We establish a sharp rate of convergence for a free-boundary curve shortening flow in a convex domain in ℝ² which converges in finite time to a round half-point.Curve shorteningSingularitiesStability & uniquenessFree boundary & capillary https://arxiv.org/abs/2404.08824arxiv:2404.08824Fri, 12 Apr 2024 00:00:00 GMTTheodora Bourni, Nathan Burns, Spencer Catron — We classify convex ancient curve shortening flows with free boundary on general bounded convex domains.Curve shorteningAncient solutionsFree boundary & capillary