https://neckpinch.com/authors/tongxin-xu/New arXiv papers by Tongxin Xu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.28238arxiv:2610.28238Tue, 20 Oct 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove that every complete Kähler–Ricci shrinker with nonnegative Ricci curvature is holomorphically isometric to ℂ^k× N^(n-k) for some 0≤ k≤ n, where ℂ^k is the Gaussian shrinker and N is a compact Kähler–Ricci shrinker with nonnegative Ricci curvature. As a corollary, every complete Kähler–Ricci shrinker with quasi-positive Ricci curvature is compact.Ricci solitonsKähler geometry https://arxiv.org/abs/2609.18834arxiv:2609.18834Wed, 16 Sep 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove that any finite-time collapsing Kähler-Ricci flow on compact Kähler surfaces develops a Type I singularity. Together with the previous results, this implies that any finite time singularity of the Kähler-Ricci flow on compact Kähler surfaces is of Type I.Ricci flowKähler–Ricci flowSingularities(Non)collapsingKähler geometry https://arxiv.org/abs/2609.01442arxiv:2609.01442Tue, 01 Sep 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove that any finite time collapsing Kähler Ricci flow on ruled surfaces develops a Type I singularity, such singularity is modeled on the standard product shrinker ℙ¹× ℂ. As an application, we obtain the optimal collapse rate of fibers on ruled surfaces.Ricci flowKähler–Ricci flowRicci solitonsSingularities(Non)collapsingKähler geometry https://arxiv.org/abs/2608.17458arxiv:2608.17458Tue, 18 Aug 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — We prove the Feldman–Ilmanen–Knopf conjecture for finite time Type I singularities of the Kähler–Ricci flow. More precisely, for any compact Kähler manifold Y and its blow-up π:BlₚY⟶ Y, if [ω₀]−Tc₁(M)=π^*[ω_Y], then any Type I parabolic blow-up limit of the Kähler Ricci flow along the exceptional divisor is the FIK shrinker Tot(𝓞_(ℙⁿ⁻¹)(−1)).Ricci flowKähler–Ricci flowRicci solitonsSingularitiesKähler geometryAnalytic minimal model program https://arxiv.org/abs/2608.10953arxiv:2608.10953Tue, 11 Aug 2026 00:00:00 GMTTongxin Xu, Zhenlei Zhang — In this paper, we study compactness, rigidity, and related geometric properties of complete Kähler Ricci shrinkers through the polarized Fano fibration structure.Ricci solitonsKähler geometryLimit spaces & RCDStability & uniquenessAnalytic minimal model program