12 citations · 30 across the 11 of their papers we have counts for
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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…
Stable minimal hypersurfaces in
Otis Chodosh, Chao Li, Paul Minter +1
We show that a complete, two-sided, stable minimal hypersurface in is flat.
Existence of closed embedded curves of constant curvature via min-max
Lorenzo Sarnataro, Douglas Stryker
We find conditions under which Almgren-Pitts min-max for the prescribed geodesic curvature functional in a closed oriented Riemannian surface produces a closed embedded curve of co…
Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies
Lorenzo Sarnataro, Douglas Stryker
We prove the optimal regularity for minimizers of the prescribed mean curvature functional over isotopy classes. As an application, we find an embedded sphere of prescrib…
Volume growth of 3-manifolds with scalar curvature lower bounds
Otis Chodosh, Chao Li, Douglas Stryker
We give a new proof of a recent result of Munteanu--Wang relating scalar curvature to volume growth on a -manifold with non-negative Ricci curvature. Our proof relies on the the…
Complete stable minimal hypersurfaces in positively curved 4-manifolds
Otis Chodosh, Chao Li, Douglas Stryker
We show that the combination of non-negative sectional curvature (or -intermediate Ricci curvature) and strict positivity of scalar curvature forces rigidity of complete (non-co…
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…
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 flo…