Author

Jian-Quan Ge

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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 Sep 2026

Total scalar curvature under a curvature operator lower bound

Let $(M^{n}, g)$ be a complete, simply connected Riemannian manifold without boundary, of dimension $n\ge3$, with curvature operator at least that of the unit sphere. We prove that $$\int_M {\rm scal}(x)\ d {\rm Vol}_x\le n(n-1)\omega_n,$$ where $\omega_n$ is the volume of the unit $n$-sphere. Equality holds if and onl...

Jian-Quan Ge, Chuan-Huan Li, Rong-Gang Li · 0 citations