4 papers · 1 filter
Stable 2-systole bounds in positive scalar curvature
Douglas Stryker
We prove that the stable 2-systole is uniformly bounded on the space of Riemannian metrics with scalar curvature at least one for closed spin 2-essential manifolds, which includes…
A spinor proof of the classification of stable minimal surfaces in
Douglas Stryker
We give a proof that every complete two-sided stable minimal surface in is flat using the index theory for Dirac operators on twisted spinor bundles.
Index, Intersections, and Multiplicity of Min-Max Geodesics
Jared Marx-Kuo, Lorenzo Sarnataro, Douglas Stryker
We prove upper bounds for the Morse index and number of intersections of min-max geodesics achieving the -widths of a closed surface. A key tool in our analysis is a proof that…
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 curv…