https://neckpinch.com/authors/jingwen-chen/New arXiv papers by Jingwen Chen, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.35000arxiv:2610.35000Mon, 26 Oct 2026 00:00:00 GMTJingwen Chen — We construct closed mean curvature flows with arbitrarily large genus increase in every smooth Riemannian three-manifold, giving counterexamples to Ilmanen's genus-reduction conjecture. We prove that a compact hypersurface with a single isolated conical singularity and a power rate of convergence to its cone admits a mean curvature flow whose forward rescaled limit is a prescribed expander in the tangent space at the singular point, smoothly asymptotic to that cone. Combining this theorem with closed mean curvature flows with prescribed tangent flows (arXiv:2405.15577, arXiv:2607.23879) and the noncompact counterexample (arXiv:2605.09657) gives the desired examples.Mean curvature flowRicci solitonsSingularities3-manifoldsBoundaries & non-compact https://arxiv.org/abs/2610.20453arxiv:2610.20453Wed, 14 Oct 2026 00:00:00 GMTJingwen Chen — In this short note, using OpenAI's resolution of the Solomon–Yau conjecture, we extend our joint work with Pedro Gaspar to all dimensions n≥2. We construct eternal Allen–Cahn flows on Sⁿ⁺¹ connecting approximations of any prescribed least-area Clifford hypersurface and equatorial sphere. We also construct infinitely many eternal integral Brakke flows from least-area Clifford hypersurfaces to equatorial spheres.Mean curvature flowWeak & singular flowsPhase fields & multiphase flows https://arxiv.org/abs/2607.23879arxiv:2607.23879Sun, 26 Jul 2026 00:00:00 GMTJingwen Chen, Tang-Kai Lee, Ao Sun, Xinrui Zhao — Given an embedded shrinker Σ in ℝⁿ⁺¹ that is either closed, asymptotically conical, or a Cartesian product of such a shrinker with ℝ^k, we construct a closed embedded mean curvature flow whose tangent flow at the first singularity is modeled on Σ. We also prescribe the first-order asymptotics of the tangent flow. This result is a consequence of a more general theorem that allows us to construct mean curvature flows with an additional force whose tangent flow and first-order asymptotics at the first singularity are prescribed.Mean curvature flowRicci solitonsSingularitiesBoundaries & non-compact https://arxiv.org/abs/2507.03837arxiv:2507.03837Fri, 04 Jul 2025 00:00:00 GMTJingwen Chen, Pedro Gaspar — From the perspective of Morse theory, it is natural to investigate gradient flow trajectories between critical points. In this short note, we explore the minimal hypersurface analogue of this phenomenon and present examples that suggest additional topological and variational obstructions to the existence of connecting mean curvature flows.Mean curvature flowMinimal & CMC surfaces https://arxiv.org/abs/2402.04521arxiv:2402.04521Wed, 07 Feb 2024 00:00:00 GMTJingwen Chen, Ao Sun — We construct new examples of immortal mean curvature flow of smooth embedded connected hypersurfaces in closed manifolds, which converge to minimal hypersurfaces with multiplicity 2 as time approaches infinity.Mean curvature flowLong-time existence & convergenceMinimal & CMC surfaces https://arxiv.org/abs/2312.17457arxiv:2312.17457Fri, 29 Dec 2023 00:00:00 GMTJingwen Chen, Ao Sun — We construct a new example of an immortal mean curvature flow of smooth embedded connected surfaces in ℝ³, which converges to a plane with multiplicity 2 as time approaches infinity.Mean curvature flowLong-time existence & convergence https://arxiv.org/abs/2304.12282arxiv:2304.12282Mon, 24 Apr 2023 00:00:00 GMTJingwen Chen — In this article, we generalize our previous results joint with Pedro Gaspar to higher dimensions, prove the existence of (infinitely many) eternal weak mean curvature flows in Sⁿ⁺¹ (for all n ≥ 2) connecting a Clifford hypersurface S¹(√(1/n)) × Sⁿ⁻¹ (√((n-1)/n)) to the equatorial spheres Sⁿ.Mean curvature flow https://arxiv.org/abs/2107.09140arxiv:2107.09140Mon, 19 Jul 2021 00:00:00 GMTJingwen Chen, Pedro Gaspar — In this article we study eternal solutions to the Allen-Cahn equation in the 3-sphere, in view of the connection between the gradient flow of the associated energy functional, and the mean curvature flow. We construct eternal integral Brakke flows that connect Clifford tori to equatorial spheres, and study a family of such flows, in particular their symmetry properties. Our approach is based on the realization of Brakke's motion by mean curvature as a singular limit of Allen-Cahn gradient flows, as studied by Ilmanen, and Tonegawa, and it uses the classification of ancient gradient flows in spheres, by K. Choi and C. Mantoulidis, as well as the rigidity of stationary solutions with low Morse index proved by F. Hiesmayr.Mean curvature flowAncient solutionsWeak & singular flowsStability & uniquenessPhase fields & multiphase flows