https://neckpinch.com/authors/goncalo-oliveira/New arXiv papers by Goncalo Oliveira, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.31343arxiv:2609.31343Fri, 25 Sep 2026 00:00:00 GMTJason D. Lotay, Goncalo Oliveira — We prove that at any nondegenerate neck pinch singularity of Lagrangian mean curvature flow of surfaces the mean curvature becomes unbounded, with control on the blow-up rate.Mean curvature flowLagrangian mean curvature flowSingularities https://arxiv.org/abs/2305.05744arxiv:2305.05744Tue, 09 May 2023 00:00:00 GMTJason D. Lotay, Goncalo Oliveira — In this article we consider the Lagrangian mean curvature flow of compact, circle-invariant, almost calibrated Lagrangian surfaces in hyperkähler 4-manifolds with circle symmetry. We show that this Lagrangian mean curvature flow can be continued for all time, through finite time singularities, and converges to a chain of special Lagrangians, thus verifying various aspects of Joyce's conjectures in this setting. We show that the singularities of the flow are neck pinches in the sense conjectured by Joyce. We also give examples where such finite time singularities are guaranteed to occur.Mean curvature flowLagrangian mean curvature flowRicci-flat & Calabi–YauSingularities4-manifoldsKähler geometry