https://neckpinch.com/authors/longteng-chen/New arXiv papers by Longteng Chen, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.19152arxiv:2608.19152Wed, 19 Aug 2026 00:00:00 GMTLongteng Chen, Max Hallgren, Lucas Lavoyer — We describe certain finite-time singularities of the Kähler-Ricci flow arising in the analytic minimal model program. Assuming that convergence to an asymptotically conical Kähler-Ricci shrinker is realized by holomorphic maps, we prove that, in a fixed holomorphic gauge, the nearby flow is modeled on the shrinker at the level of Kähler potentials. Consequently, every noncollapsed Kähler-Ricci flow through singularities in complex dimension two is modeled on a shrinker-cone-expander transition, confirming a strong form of Song's conjectural picture. We also show analogous results in higher dimensions under the Calabi ansatz, and improve known results in the compact shrinker case. These give the first compact Ricci flows through conical singularities whose small-scale behavior is fully described.Ricci flowKähler–Ricci flowRicci solitonsSingularities(Non)collapsingKähler geometryWeak & singular flowsBoundaries & non-compactAnalytic minimal model program https://arxiv.org/abs/2606.08837arxiv:2606.08837Sun, 07 Jun 2026 00:00:00 GMTLongteng Chen — In this paper, we investigate the relationship between the long time behaviour of solutions to the Kahler-Ricci flow on an asymptotically conical gradient Kahler-Ricci expander and the asymptotic behaviour of their initial data at spatial infinity.Ricci flowKähler–Ricci flowRicci solitonsKähler geometryBoundaries & non-compactLong-time existence & convergence https://arxiv.org/abs/2604.04223arxiv:2604.04223Sun, 05 Apr 2026 00:00:00 GMTLongteng Chen, Max Hallgren, Lucas Lavoyer — Let (Y,g₀) be a compact analytic space with a finite number of singular points, where the metric at each singular point is modelled on a Kähler cone with smooth canonical model. We show that the Kähler-Ricci flow with such initial data satisfies a C/t curvature bound, and that the flow near each singular point is modelled on the unique Kähler-Ricci expander asymptotic to the corresponding cone. Our motivation is to give a geometric description of the Kähler–Ricci flow emerging from singularities arising in the analytic minimal model program.Ricci flowKähler–Ricci flowRicci solitonsSingularitiesKähler geometryAnalytic minimal model program https://arxiv.org/abs/2510.06850arxiv:2510.06850Wed, 08 Oct 2025 00:00:00 GMTLongteng Chen — In this work, we consider a perturbation of an asymptotically conical gradient expanding Kähler-Ricci soliton metric g in the same Kähler class. We demonstrate that, under suitable assumptions, the normalized Kähler-Ricci flow starting from the initial perturbed metric exists for all time and converges uniformly to an asymptotically conical gradient expanding Kähler-Ricci soliton metric g_∞. Moreover, if the perturbed initial metric is asymptotic to g at spatial infinity, then the limiting metric coincides with the original soliton, that is, g_∞ = g.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsKähler geometryStability & uniquenessBoundaries & non-compactLong-time existence & convergence https://arxiv.org/abs/2505.00167arxiv:2505.00167Wed, 30 Apr 2025 00:00:00 GMTLongteng Chen — We study the uniqueness problem for the Kähler-Ricci flow with a conical initial condition. Given a complete gradient expanding Kähler-Ricci soliton on a non compact manifold with quadratic curvature decay, including its derivatives, we establish that any complete solution to the Kahler-Ricci flow emerging from the soliton's tangent cone at infinity–appearing as a Kähler cone–must coincide with the forward self-similar Kähler-Ricci flow associated with the soliton, provided certain conditions hold. Specifically, if its Kähler form remains in the same cohomology class as that of the soliton's self-similar Kähler-Ricci flow, its full Riemann curvature operator is bounded for each fixed positive time, its Ricci curvature is bounded from above by A/t, its scalar curvature is bounded from below by -A/t, and it shares a same Killing vector field with the soliton metric. This paper gives a partial answer to a question in paper of Feldman-Ilmanen-Knopf, and generalizes the earlier work of Conlon-Deruelle and the work of Conlon-Deruelle-Sun.Ricci flowKähler–Ricci flowRicci solitonsKähler–Ricci solitonsKähler geometryScalar curvatureStability & uniquenessBoundaries & non-compact