https://neckpinch.com/authors/ettore-lo-giudice/New arXiv papers by Ettore Lo Giudice, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2510.08846/arxiv:2510.08846Thu, 09 Oct 2025 00:00:00 GMTEttore Lo Giudice — We study the positive Hermitian curvature flow for left-invariant metrics on 2-step nilpotent Lie groups with a left-invariant complex structure J. We describe the long-time behavior of the flow under the assumption that J[g, g] is contained in the center of g. We show that under our assumption the flow gₜ exists for all positive t and (G,(1+t)⁻¹gₜ) converges, in the Cheeger-Gromov topology, to a 2-step nilpotent Lie group with a non flat semi-algebraic soliton. Moreover, we prove that, in our class of Lie groups, there exists at most one semi-algebraic soliton solution, up to homothety. Similar results were proved by M. Pujia and J. Stanfield for nilpotent complex Lie groups. In the last part of the paper we study the Hermitian curvature flow for the same class of Lie groups.Generalized & G₂ flowsHomogeneous spacesLong-time existence & convergence