Author

Yu-Hang Liu

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Preprint Oct 2026

Orbit stratifications and smooth topology of positively curved six-manifolds with rank-one nonabelian symmetry

We study closed simply connected six-manifolds with positive sectional curvature and an effective isometric action of $SO(3)$ or $SU(2)$. Starting from Liu's corrected orbit-space analysis, we refine the stratification and recover smooth topology in several previously unresolved cases. For a boundaryless $SO(3)$ quotie...

Min-Bo Gao, Yu-Hang Liu · 0 citations

Preprint Aug 2026

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...

Yu-Hang Liu · 0 citations