Research profile

Douglas Stryker

Works on curve shortening, ancient solutions and mean curvature flow.

NP-RC-272760

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Curve shorteningAncient solutionsMean curvature flowSingularitiesStability & uniqueness

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  1. Ao Sun

    2 joint workslatest 2019

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2019

math.DGWider flowsv2arXiv:1909.02535

Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at

Douglas 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 -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
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math.DGWider flowsv2arXiv:1908.02688

Construction of High Codimension Ancient Mean Curvature Flows

Douglas 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
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NP-RC-272760 is Douglas Stryker's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.

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