https://neckpinch.com/authors/yingxiang-hu/New arXiv papers by Yingxiang Hu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2408.06057/arxiv:2408.06057Mon, 12 Aug 2024 00:00:00 GMTYingxiang Hu, Mohammad N. Ivaki — In the first part of this paper, we study the following non-homogeneous, locally constrained inverse curvature flow in Euclidean space ℝⁿ⁺¹, \beginalign* \dotx=\left(\frac1{\frac{E_k(\hatκ)}{E_k-1(\hatκ)}-α}-\langle x,ν\rangle\right)ν, \quad k=2,3,\ldots,n-1. \endalign* Assuming that the initial hypersurface 𝓜₀ ⊂ ℝⁿ⁺¹ is star-shaped and its shifted principal curvatures hatκ=κ+α(1,…,1) lie in the convex set \beginalign* Γ_α,k:=Γ_k-1\cap \{λ\in \mathbbR^n:\, E_k(λ)-αE_k-1(λ)>0\}, \endalign* we show that the flow admits a smooth solution that exists for all positive times, and it converges smoothly to a round sphere. As a corollary, we obtain a new set of Alexandrov-Fenchel-type inequalities for non-convex domains. In the second part, we derive a Poincaré type inequality for k-convex hypersurfaces which complements a more general version of the well-known Heintze-Karcher inequality.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsHomogeneous spacesLong-time existence & convergenceGeometric inequalities https://neckpinch.com/papers/2209.12479/arxiv:2209.12479Mon, 26 Sep 2022 00:00:00 GMTYingxiang Hu, Yong Wei, Bo Yang, Tailong Zhou — In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with θ-capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle θ∈ (0,π/2]. We prove that the solution of the flow remains to be strictly convex for t>0, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space with the contact angle θ∈(0,π/2]. Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsBoundaries & non-compactFree boundary & capillaryLong-time existence & convergenceGeometric inequalities