https://neckpinch.com/authors/alessandro-pigati/New arXiv papers by Alessandro Pigati, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2307.15134/arxiv:2307.15134Thu, 27 Jul 2023 00:00:00 GMTDavide Parise, Alessandro Pigati, Daniel Stern — We develop the asymptotic analysis as ε→ 0 for the natural gradient flow of the self-dual U(1)-Higgs energies E_ε(u,∇)=∫_M(|∇u|²+ε²|F_∇|²+((1-|u|²)²)/(4ε²)) on Hermitian line bundles over closed manifolds (Mⁿ,g) of dimension n≥ 3, showing that solutions converge in a measure-theoretic sense to codimension-two mean curvature flows – i.e., integral (n-2)-Brakke flows – generalizing results of the last two authors from the stationary case. Given any integral (n-2)-cycle Γ₀ in M, these results can be used together with the convergence theory developed in previous work of the authors to produce nontrivial integral Brakke flows starting at Γ₀ with additional structure, similar to those produced via Ilmanen's elliptic regularization.Mean curvature flowWeak & singular flows