https://neckpinch.com/authors/kevin-sonnanburg/New arXiv papers by Kevin Sonnanburg, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1711.02261/arxiv:1711.02261Tue, 07 Nov 2017 00:00:00 GMTKevin Sonnanburg — Ancient solutions arise in the study of parabolic blow-ups. If we can categorize ancient solutions, we can better understand blow-up limits. Based on an argument of Giga and Kohn, we give a Liouville-type theorem restricting ancient, type-I, non-collapsing two- dimensional mean curvature flows to either spheres or cylinders.Mean curvature flowAncient solutionsSingularities(Non)collapsingSurfaces https://neckpinch.com/papers/1703.02619/arxiv:1703.02619Tue, 07 Mar 2017 00:00:00 GMTKevin Sonnanburg — Under mean curvature flow, a closed, embedded hypersurface M(t) becomes singular in finite time. For certain classes of mean-convex mean curvature flows, we show the continuity of the first singular time T and the limit set "M(T)", with respect to initial data. We employ an Angenent-like neck-pinching argument to force singularities in nearby flows. However, since we cannot prescribe initial data, we combine Andrews' α-non-collapsed condition and Colding and Minicozzi's uniqueness of tangent flows to place appropriately sized spheres in the region inside the hypersurface.Mean curvature flowSingularities(Non)collapsingCurvature pinchingStability & uniqueness