https://neckpinch.com/authors/xiang-li/New arXiv papers by Xiang Li, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2609.18064/arxiv:2609.18064Wed, 16 Sep 2026 00:00:00 GMTLi Xiang, Sun Jun — A λ-translating soliton is a hypersurface in ℝⁿ⁺¹ satisfying H=⟨ T,ν⟩+λ; equivalently, it has constant weighted mean curvature with respect to the log-linear density e^(⟨ T,X⟩), and is an eternal solution of the mean curvature flow with a constant forcing term. In this paper, we first prove that every complete properly immersed λ-translating soliton with λ>0 and inf_ΣH>λ has at least exponential volume growth, in contrast with the linear growth of ordinary translating solitons. We then prove sharp non-existence results for graphic λ-translating solitons (λgeqslant 0) with bounded gradient, and two rigidity theorems.Mean curvature flowAncient solutionsSelf-shrinkers & translatorsStability & uniqueness https://neckpinch.com/papers/2412.15880/arxiv:2412.15880Fri, 20 Dec 2024 00:00:00 GMTXiang Li, Yong Luo, Jun Sun — In this paper, we will prove some rigidity theorems for blow up limits to Type II singularities of Lagrangian mean curvature flow with zero Maslov class or almost calibrated Lagrangian mean curvature flows, especially for Lagrangian translating solitons in any dimension. These theorems generalized previous corresponding results from two dimensional case to arbitrarily dimensional case.Mean curvature flowLagrangian mean curvature flowSelf-shrinkers & translatorsSingularitiesSurfacesStability & uniqueness