https://neckpinch.com/authors/eugenio-vecchi/New arXiv papers by Eugenio Vecchi, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2406.15123/arxiv:2406.15123Fri, 21 Jun 2024 00:00:00 GMTAdriano Pisante, Eugenio Vecchi — We consider the inverse mean curvature flow (IMCF) in the Heisenberg group (Heⁿ, d_ε), where d_ε is distance associated to either | · |_ε, ε>0, the natural family of left-invariant Riemannian metrics, or with their sub-Riemannian counterparts for ε=0. For Ω⊆ Heⁿ an open set with smooth boundary Σ₀=∂Ω satisfying a uniform exterior gauge-ball condition and bounded complement we show existence of a global weak IMCF of generalized hypersurfaces \Σ^εₛ\_(s ≥ 0) ⊆ ℍⁿ which are level sets of a proper globally Lipschitz function with logarithmic growth at infinity. Here, both in the Riemannian and in the sub-Riemannian setting, we adopt the weak formulation introduced by Huisken and Ilmanen in, following the approach in due to Moser and based on the the link between IMCF and p-harmonic functions.Mean curvature flowOther curvature flowsInverse mean curvature flowWeak & singular flows