https://neckpinch.com/authors/adam-jacob/New arXiv papers by Adam Jacob, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2405.11049/arxiv:2405.11049Fri, 17 May 2024 00:00:00 GMTTristan C. Collins, Adam Jacob, Yu-Shen Lin — We establish a convergence result for the mean curvature flow starting from a totally real submanifold which is "almost minimal" in a precise, quantitative sense. This extends, and makes effective, a result of H. Li for the Lagrangian mean curvature flow.Mean curvature flowLagrangian mean curvature flow https://neckpinch.com/papers/2310.17709/arxiv:2310.17709Thu, 26 Oct 2023 00:00:00 GMTYu Hin Chan, Adam Jacob — The line bundle mean curvature flow is a complex analogue of the mean curvature flow for Lagrangian graphs, with fixed points solving the deformed Hermitian-Yang-Mills equation. In this paper we construct two distinct examples of singularities along the flow. First, we find a finite time singularity, ruling out long time existence of the flow in general. Next we show long time existence of the flow with a Calabi symmetry assumption on the blowup of ℙⁿ, n≥ 3, if one assumes supercritical phase. Using this, we find an example where a singularity occurs at infinite time along the destabilizing subvariety in the semi-stable case.Mean curvature flowLagrangian mean curvature flowSingularitiesKähler geometryLong-time existence & convergence