https://neckpinch.com/authors/douglas-stryker/New arXiv papers by Douglas Stryker, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1909.02535/arxiv:1909.02535Thu, 05 Sep 2019 00:00:00 GMTDouglas Stryker, Ao Sun — Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, we prove codimension bounds for ancient mean curvature flows by their tangent flow at -∞, generalizing a theorem for cylinders in [CM19b]. In the case of the m-covered circle, we apply this bound to prove a strong rigidity theorem. Furthermore, we extend this paradigm by showing that under the assumption of sufficiently rapid convergence, a compact ancient mean curvature flow is identical to its tangent flow at -∞.Mean curvature flowCurve shorteningAncient solutionsSingularitiesStability & uniqueness https://neckpinch.com/papers/1908.02688/arxiv:1908.02688Wed, 07 Aug 2019 00:00:00 GMTDouglas Stryker, Ao Sun — We construct a class of compact ancient solutions to the mean curvature flow in Euclidean space with high codimension. In particular, we construct higher codimensional ancient curve shortening flows. Moreover, we characterize the asymptotic behavior of these solutions. Add on remark: the construction in this paper has been discovered by Altschuler D.-Altschuler S.-Angenent-Wu in [AAAW13].Mean curvature flowCurve shorteningAncient solutions