https://neckpinch.com/authors/jesse-madnick/New arXiv papers by Jesse Madnick, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2208.01574/arxiv:2208.01574Tue, 02 Aug 2022 00:00:00 GMTJesse Madnick, Albert Wood — We study mean curvature flow of Lagrangians in ℂⁿ that are cohomogeneity-one with respect to a compact Lie group G ≤ SU(n) acting linearly on ℂⁿ. Each such Lagrangian necessarily lies in a level set μ⁻¹(ξ) of the standard moment map μcolon ℂⁿ → g^*, and mean curvature flow preserves this containment. We classify all cohomogeneity-one self-similarly shrinking, expanding and translating solutions to the flow, as well as cohomogeneity-one smooth special Lagrangians lying in μ⁻¹(0). Restricting to the case of almost-calibrated flows in the zero level set μ⁻¹(0), we classify finite-time singularities, explicitly describing the Type I and Type II blowup models. Finally, given any cohomogeneity-one special Lagrangian in μ⁻¹(0), we show it occurs as the Type II blowup model of a Lagrangian MCF singularity. Throughout, we give explicit examples of suitable group actions, including a complete list in the case of G simple. This yields infinitely many new examples of shrinking and expanding solitons for Lagrangian MCF, as well as infinitely many new singularity models.Mean curvature flowLagrangian mean curvature flowRicci solitonsSelf-shrinkers & translatorsSingularitiesHomogeneous spaces