https://neckpinch.com/authors/ruijia-zhang/New arXiv papers by Ruijia Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2611.03249/arxiv:2611.03249Mon, 02 Nov 2026 00:00:00 GMTTianci Luo, Yong Wei, Ruijia Zhang, Rong Zhou — We prove that every smooth closed strictly convex hypersurface in ℝⁿ⁺¹ contracts to a round point under the σₖ-curvature flow for 2≤ k≤ n-1, without additional pinching or symmetry assumptions. After rescaling about the extinction point to mean width two, the hypersurfaces converge smoothly and exponentially in normalized time to the unit sphere. The proof is based on an entropy which is invariant under translations and dilations and admits a representation by weighted boundary areas of orthogonal projections. A strengthened Codazzi inequality yields its monotonicity. An upper bound for the entropy controls the inradius relative to the mean width, while its dissipation controls the spatial variation of the normalized speed. We also obtain two-sided curvature bounds at the natural extinction scale.Other curvature flowsCurvature pinchingLong-time existence & convergence https://neckpinch.com/papers/2610.35707/arxiv:2610.35707Mon, 26 Oct 2026 00:00:00 GMTTianci Luo, Yong Wei, Ruijia Zhang, Rong Zhou — We study quermassintegral-preserving curvature flows in ℍⁿ⁺¹, n≥3, driven by the curvature quotient (Eₖ/E_ℓ)^(1/(k-ℓ)). For 1≤ℓ<k with k+ℓ≤ n, we prove that positive sectional curvature is preserved. Starting from a smooth closed strictly convex hypersurface with positive sectional curvature, the flow exists for all time and converges smoothly and exponentially to a geodesic sphere. As an application, we establish sharp Alexandrov–Fenchel inequalities between Wₖ and W_ℓ for smooth bounded convex domains whose boundaries have nonnegative sectional curvature, whenever 0≤ℓ<k≤ n and k+ℓ≤ n. Equality holds if and only if the domain is a geodesic ball. Together with previously known cases, these inequalities give the full family of Alexandrov–Fenchel inequalities for this class of domains in ℍ⁶. We also construct counterexamples showing that k+ℓ≤ n is the optimal range for preservation of positive sectional curvature by these flows.Other curvature flowsSphere theoremsLong-time existence & convergenceGeometric inequalities