https://neckpinch.com/authors/ben-lambert/New arXiv papers by Ben Lambert, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.32819arxiv:2610.32819Fri, 23 Oct 2026 00:00:00 GMTBen S. Lambert, Oliver C. Schnürer — We study rotationally symmetric graphical solutions to mean curvature flow that are initially close to a homothetic reference expander, in particular near infinity. Based on a computer algebra aided proof, we show that under appropriate conditions, at large times, the solutions are closer to a different expander than to the reference expander.Mean curvature flowRicci solitonsRotational symmetry & warped products https://arxiv.org/abs/2304.02414arxiv:2304.02414Wed, 05 Apr 2023 00:00:00 GMTWilhelm Klingenberg, Ben Lambert, Julian Scheuer — Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical with respect to its rays. Its boundary is required to have constant intersection angle with the boundary of the cone. We prove that the corresponding parabolic boundary value problem for the graph admits a solution for all time which rescales to a self-similarly expanding solution.Mean curvature flow3-manifoldsFree boundary & capillaryPhysics https://arxiv.org/abs/2207.01123arxiv:2207.01123Sun, 03 Jul 2022 00:00:00 GMTBen Lambert, Elena Mäder-Baumdicker — We obtain estimates on nonlocal quantities appearing in the Volume Preserving Mean Curvature Flow (VPMCF) in the closed, Euclidean setting. As a result we demonstrate that blowups of finite time singularities of VPMCF are ancient solutions to Mean Curvature Flow (MCF), prove that monotonicity methods may always be applied at finite times and obtain information on the asymptotics of the flow.Mean curvature flowVolume-preserving & constrained flowsAncient solutionsSingularities https://arxiv.org/abs/2206.14060arxiv:2206.14060Tue, 28 Jun 2022 00:00:00 GMTBen Lambert, Elena Mäder-Baumdicker — We demonstrate that the property of being Alexandrov immersed is preserved along mean curvature flow. Furthermore, we demonstrate that mean curvature flow techniques for mean convex embedded flows such as noncollapsing and gradient estimates also hold in this setting. We also indicate the necessary modifications to the work of Brendle–Huisken to allow for mean curvature flow with surgery for the Alexandrov immersed, 2-dimensional setting.Mean curvature flowSurgery(Non)collapsing