https://neckpinch.com/authors/guoxin-wei/New arXiv papers by Guoxin Wei, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.24431arxiv:2609.24431Mon, 21 Sep 2026 00:00:00 GMTZhishuai Liu, Guoxin Wei — In this paper, we study the anisotropic-length-preserving weighted anisotropic curvature flow for smooth convex closed plane curves. For any smooth, embedded, closed, convex initial curve, the flow exists smoothly for all time, and the anisotropic curvature converges smoothly to that of the boundary of the corresponding homothetic Wulff shape as time tends to infinity.Other curvature flowsAnisotropic & nonlocal flowsLong-time existence & convergence https://arxiv.org/abs/2609.20429arxiv:2609.20429Thu, 17 Sep 2026 00:00:00 GMTZhi Li, Guoxin Wei — Our first main result is a rigidity theorem for complete self-expanders in the Euclidean space with higher codimension, assuming an integral cur More precisely, any smooth complete self-expander x:M→ ℝ^(n+p)(n≥3) that satisfies both (∫_M|A|ⁿdμ)^(1/n)<K(n) and ∫_M|A|ⁿe^(frac|x|²2)dμ<∞ for a positive constant K(n) depending only o isometric to ℝⁿ. Moreover, we show that the rigidity result persists when the pinching condition is expressed in terms of the trace-free second fundamental form.Mean curvature flowSelf-shrinkers & translatorsCurvature pinchingStability & uniqueness https://arxiv.org/abs/2609.01346arxiv:2609.01346Tue, 01 Sep 2026 00:00:00 GMTHaoxuan Cheng, Junqi Lai, Guoxin Wei — For every pair of integers 3≤ k<n with k odd, we construct a compact embedded rotational torus in ℝⁿ⁺¹ whose homothetic dilations satisfy the unnormalised σₖ-curvature flow in a Sobolev almost-everywhere sense. Its profile curve has Hölder regularity C^(1,1/k) and Sobolev regularity W^(2,p) for every 1≤ p<k/(k-1). Away from two singular latitudes the torus is smooth; globally, the flow equation is interpreted using the weak shape operator of the associated Lipschitz boundary. Under rotational symmetry, the self-similar equation ⟨ X,ν⟩=−σₖ, where X is the position vector and ν is the unit normal, reduces to a degenerate profile system. We solve this system by combining an odd-power desingularisation, a shooting argument, uniform radial and axial bounds, and a strict gap between the shooting parameters and the cylindrical radius. No classical C² rotational torus can satisfy the soliton equation, so the loss of regularity is unavoidable within the rotational toroidal class.Other curvature flowsRotational symmetry & warped products https://arxiv.org/abs/2604.11443arxiv:2604.11443Mon, 13 Apr 2026 00:00:00 GMTZhishuai Liu, Guoxin Wei — In this paper, we study the area-preserving and length-preserving κ^α-type curvature flows of smooth, closed, convex curves in the two-dimensional hyperbolic plane ℍ² for α<0 and prove that convexity is preserved along the flows. Assuming that the flows exist for all time, we show that the evolving curves converge smoothly to geodesic circles. Furthermore, we also derive a sufficient condition for global existence of the flows.Other curvature flowsInverse mean curvature flowVolume-preserving & constrained flowsSurfacesLong-time existence & convergence https://arxiv.org/abs/2406.11123arxiv:2406.11123Mon, 17 Jun 2024 00:00:00 GMTQing-Ming Cheng, Junqi Lai, Guoxin Wei — In the paper, we construct, for λ>0, complete embedded and non-convex λ-hypersurfaces, which are diffeomorphic to a cylinder. Hence, one can not expect that λ-hypersurfaces share a common conclusion on the planar domain conjecture even if the planar domain conjecture of T. Ilmanen for self-shrinkers of mean curvature flow are solved by Brendle affirmatively. Furthermore, for a fixed λ<0 which may have small |λ|, we can construct two compact embedded λ-hypersurfaces which are diffeomorphic to S¹× Sⁿ⁻¹, but they are not isometric to each other.Mean curvature flowSelf-shrinkers & translators