https://neckpinch.com/authors/lucas-lavoyer/New arXiv papers by Lucas Lavoyer, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.21472arxiv:2609.21472Fri, 18 Sep 2026 00:00:00 GMTLucas Lavoyer, Adam Thompson — We prove linear stability of all steady and expanding gradient Kähler-Ricci solitons. In the expanding case, we prove strict linear stability under very general assumptions. In particular, every asymptotically conical expanding gradient Kähler-Ricci soliton is strictly linearly stable.Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniquenessBoundaries & non-compact 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/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/2509.25081arxiv:2509.25081Mon, 29 Sep 2025 00:00:00 GMTLucas Lavoyer, Luke T. Peachey — We find new examples of steady gradient Ricci solitons with positive curvature operator in dimensions four and above. Utilising a procedure first introduced by Lai, we construct examples with O(p) × O(q) symmetry in dimension p+q for any pair of integers p,q ≥ 2 and discuss their asymptotic geometry.Ricci solitonsSphere theorems https://arxiv.org/abs/2305.00344arxiv:2305.00344Sat, 29 Apr 2023 00:00:00 GMTLucas Lavoyer — We study the Ricci flow out of spaces with edge type conical singularities along a closed, embedded curve. Under the additional assumption that for each point of the curve, our space is locally modelled on the product of a fixed positively curved cone and a line, we show existence of a solution to Ricci flow (M,g(t)) for t∈ (0,T], which converges back to the singular space as t↘ 0 in the pointed Gromov-Hausdorff topology. We also prove curvature estimates for the solution and, for edge points, we show that the tangent flow at these points is a positively curved expanding Ricci soliton solution crossed with a line.Ricci flowRicci solitonsSingularitiesWeak & singular flowsLimit spaces & RCD