https://neckpinch.com/authors/hui-ma/New arXiv papers by Hui Ma, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1802.03521/arxiv:1802.03521Sat, 10 Feb 2018 00:00:00 GMTShanze Gao, Hui Ma — In this paper we study self-similar solutions in warped products satisfying F-𝓕=g(λ(r)∂ᵣ,ν), where 𝓕 is a nonnegative constant and F is in a class of general curvature functions including powers of mean curvature and Gauss curvature. We show that slices are the only closed strictly convex self-similar solutions in the hemisphere for such F. We also obtain a similar uniqueness result in hyperbolic space ℍ³ for Gauss curvature F and 𝓕≥ 1.Other curvature flowsStability & uniquenessRotational symmetry & warped products https://neckpinch.com/papers/1701.02642/arxiv:1701.02642Tue, 10 Jan 2017 00:00:00 GMTShanze Gao, Haizhong Li, Hui Ma — By adapting the test functions introduced by Choi-Daskaspoulos and Brendle-Choi-Daskaspoulos and exploring properties of the k-th elementary symmetric functions σₖ intensively, we show that for any fixed k with 1≤ k≤ n-1, any strictly convex closed hypersurface in ℝⁿ⁺¹ satisfying σₖ^α=⟨ X,ν⟩, with α≥ 1/k, must be a round sphere. In fact, we prove a uniqueness result for any strictly convex closed hypersurface in ℝⁿ⁺¹ satisfying F+C=⟨ X,ν⟩, where F is a positive homogeneous smooth symmetric function of the principal curvatures and C is a constant.Other curvature flowsHomogeneous spacesStability & uniqueness https://neckpinch.com/papers/1611.07597/arxiv:1611.07597Wed, 23 Nov 2016 00:00:00 GMTShanze Gao, Hui Ma — In this paper, employing a new inequality, we show that under certain curvature pinching condition, the strictly convex closed smooth self-similar solution of σₖ^α-flow must be a round sphere. We also obtain a similar result for the solutions of F=-⟨ X, eₙ₊₁⟩ (*) with a non-homogeneous function F. At last, we prove that if F can be compared with frac(n-k+1)σₖ₋₁kσₖ, then a closed strictly k-convex solution of (*) must be a round sphere.Other curvature flowsCurvature pinchingHomogeneous spaces