Author

Rong Zhou

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Preprint Sep 2026

Alexandrov--Fenchel inequalities for convex domains in the sphere

We prove the Alexandrov--Fenchel inequalities between any two spherical quermassintegrals for smooth weakly convex domains contained in an open hemisphere, with equality if and only if the domain is a geodesic ball. For strictly convex hypersurfaces, we introduce a globally constrained curvature flow which preserves on...

Tian-Ci Luo, Yong Wei, Rong Zhou · 0 citations

Preprint Aug 2026

Positive $\tau$-bi-Ricci curvature and Mean curvature flow with surgery in hyperbolic space

Let $n\geq3$ and $0\leq\tau\leq2$. We prove that every smooth closed connected immersed hypersurface in hyperbolic space whose induced metric has positive $\tau$-bi-Ricci curvature admits a mean curvature flow with surgery which has only finitely many surgery times and terminates. In the range compatible with cylindric...

Tian-Ci Luo, Yong Wei, Rong Zhou · 0 citations

Preprint Jul 2026

Free boundary flows by powers of the Gauss curvature in the unit ball

We study smooth compact strictly convex hypersurfaces in the unit ball that meet the support sphere orthogonally and evolve by the $\alpha$-Gauss curvature flow $\partial_tX=-K^\alpha\nu$, $\alpha>0$. We prove that the solution remains strictly convex, becomes extinct in finite time and contracts to a single point on t...

Tianci Luo, Yong Wei, Rong Zhou · 0 citations