Author

Chao Qian

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Preprint Oct 2026

Collapse to nonsmoothable manifolds under lower sectional and positive Ricci curvature bounds

We construct smooth collapsing sequences with sectional curvature at least $-1$ whose limits are topological manifolds with nonzero Kirby--Siebenmann class. For every $n\geq6$, the source and limit are simply connected, have dimensions $n+3$ and $n$, and the metrics have a common positive Ricci lower bound. The limits...

Jian-Quan Ge, Chao Qian · 0 citations

Preprint Oct 2026

On the Bryant conjecture for minimal hypersurfaces in $S^4$

We prove that a local minimal hypersurface $M^3$ in the unit sphere $S^4$ with constant scalar curvature and three distinct principal curvatures at every point must be locally congruent to the minimal Cartan isoparametric hypersurface in $S^4$, which provides a positive answer to the Bryant conjecture \cite{ChangLocal}...

Chao Qian, Ya Tao · 0 citations