Yu-Hang Liu

A Smooth Nonnegatively Curved Sphere Whose Zero-Curvature Point Locus Has Hausdorff Dimension 1/2

For every integer $m\geq 3$, we construct a smooth Riemannian metric $g$ on a manifold diffeomorphic to $S^m$ such that $\text{sec}_g\geq 0$, every sectional curvature is strictly positive away from a closed nowhere-dense set, and the point locus on which some sectional curvature vanishes has Hausdorff dimension exactl...