https://neckpinch.com/authors/matteo-novaga/New arXiv papers by Matteo Novaga, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.20054arxiv:2610.20054Wed, 14 Oct 2026 00:00:00 GMTA. Cesaroni, M. Novaga, P. Pozzi — The horizontal mean curvature flow is a geometric evolution associated with the horizontal perimeter in sub-Riemannian spaces. In this paper, we introduce a minimizing movement scheme for this flow in the first Heisenberg group ℍ, and prove the existence of a flat flow which is locally 1/2-Hölder continuous in time, with respect to the L¹-distance. The construction applies to arbitrary bounded sets of finite horizontal perimeter and does not require smoothness or symmetry of the initial datum.Mean curvature flowWeak & singular flows https://arxiv.org/abs/2601.04385arxiv:2601.04385Wed, 07 Jan 2026 00:00:00 GMTGiovanni Bellettini, Virginia Lorenzini, Matteo Novaga, Riccardo Scala — We consider a fourth-order regularization of the curvature flow for an immersed plane curve with fixed boundary, using an elastica-type functional depending on a small positive parameter ε. We show that the approximating flow smoothly converges, as ε→ 0⁺, to the curvature flow of the curve with Dirichlet boundary conditions for all times before the first singularity of the limit flow.Other curvature flowsSingularitiesBoundaries & non-compact https://arxiv.org/abs/2310.05596arxiv:2310.05596Mon, 09 Oct 2023 00:00:00 GMTMichael Gößwein, Matteo Novaga, Paola Pozzi — In this article we study the anisotropic curve shortening flow for a planar network of three curves with fixed endpoints and which meet in a triple junction. We show that the anisotropic curvature energy fulfills a Lojasiewicz-Simon gradient inequality and use this knowledge to derive stability results for the flow. Precisely, in our main theorem we show that for any initial data, which are C^(2,α)-close to a (local) energy minimizer, the flow exists globally and converges to a possibly different energy minimum.Curve shorteningAnisotropic & nonlocal flowsStability & uniquenessPhase fields & multiphase flows https://arxiv.org/abs/2207.03879arxiv:2207.03879Fri, 08 Jul 2022 00:00:00 GMTCarlo Mantegazza, Matteo Novaga, Alessandra Pluda — The motion by curvature of networks is the generalization to finite union of curves of the curve shortening flow. This evolution has several peculiar features, mainly due to the presence of junctions where the curves meet. In this paper we show that whenever the length of one single curve vanishes and two triple junctions coalesce, then the curvature of the evolving networks remains bounded. This topological singularity is exclusive of the network flow and it can be referred as a Type-0 singularity, in contrast to the well known Type-I and Type-II ones of the usual mean curvature flow of smooth curves or hypersurfaces, characterized by the different rates of blow up of the curvature. As a consequence, we are able to give a complete description of the evolution of tree-like networks till the first singular time, under the assumption that all the tangents flows have unit multiplicity. If the lifespan of such solutions is finite, then the curvature of the network remains bounded and we can apply the results by Ilmanen-Neves-Schulze/Lira-Mazzeo-Pluda-Saez to restart the flow after the singularity.Mean curvature flowCurve shorteningSingularitiesPhase fields & multiphase flows https://arxiv.org/abs/2204.04923arxiv:2204.04923Mon, 11 Apr 2022 00:00:00 GMTAnnalisa Cesaroni, Matteo Novaga — We consider the volume constrained fractional mean curvature flow of a nearly spherical set, and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data, under the assumption of global existence. Similarly, we show exponential convergence to a constant for the fractional mean curvature flow of a periodic graph.Mean curvature flowAnisotropic & nonlocal flowsStability & uniquenessLong-time existence & convergence https://arxiv.org/abs/2107.12082arxiv:2107.12082Mon, 26 Jul 2021 00:00:00 GMTAnnalisa Cesaroni, Heiko Kroener, Matteo Novaga — In this paper we discuss existence, uniqueness and some properties of a class of solitons to the anisotropic mean curvature flow, i.e., graphical translators, either in the plane or under an assumption of cylindrical symmetry on the anisotropy and the mobility. In these cases, the equation becomes an ordinary differential equation, and this allows to find explicitly the translators and describe their main features.Mean curvature flowAnisotropic & nonlocal flowsSelf-shrinkers & translatorsStability & uniqueness