https://neckpinch.com/authors/andrea-kubin/New arXiv papers by Andrea Kubin, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2508.03134arxiv:2508.03134Tue, 05 Aug 2025 00:00:00 GMTAndrea Kubin, Domenico Angelo La Manna, Enrico Pasqualetto — In this article, we introduce a variational algorithm, in the spirit of the minimizing movements scheme, to model the volume-preserving anisotropic mean curvature flow in 2D. We show that this algorithm can be used to prove the existence of classical solutions. Moreover, we prove that this algorithm converges to the global solution of the equation.Mean curvature flowVolume-preserving & constrained flowsAnisotropic & nonlocal flowsWeak & singular flowsLong-time existence & convergence https://arxiv.org/abs/2403.05947arxiv:2403.05947Sat, 09 Mar 2024 00:00:00 GMTMarco Cicalese, Andrea Kubin — We investigate the area-preserving mean-curvature-type motion of a two-dimensional lattice crystal obtained by coupling constrained minimizing movements scheme introduced by Almgren, Taylor and Wang with a discrete-to-continuous analysis. We first examine the continuum counterpart of the model and establish the existence and uniqueness of the flat flow, originating from a rectangle. Additionally, we characterize the governing system of ordinary differential equations. Subsequently, in the atomistic setting, we identify geometric properties of the discrete-in-time flow and describe the governing system of finite-difference inclusions. Finally, in the limit where both spatial and time scales vanish at the same rate, we prove that a discrete-to-continuum evolution is expressed through a system of differential inclusions which does never reduce to a system of ODEs.Mean curvature flowVolume-preserving & constrained flowsSurfacesWeak & singular flowsStability & uniqueness https://arxiv.org/abs/2305.11100arxiv:2305.11100Thu, 18 May 2023 00:00:00 GMTDaniele De Gennaro, Antonia Diana, Andrea Kubin, Anna Kubin — We prove that, in the flat torus and in any dimension, the volume-preserving mean curvature flow and the surface diffusion flow, starting C^(1,1)-close to a strictly stable critical set of the perimeter E, exist for all times and converge to a translate of E exponentially fast as time goes to infinity.Mean curvature flowVolume-preserving & constrained flowsStability & uniquenessLong-time existence & convergence https://arxiv.org/abs/2204.07450arxiv:2204.07450Fri, 15 Apr 2022 00:00:00 GMTDe Gennaro Daniele, Andrea Kubin, Anna Kubin — We characterize the long time behaviour of a discrete-in-time approximation of the volume preserving fractional mean curvature flow. In particular, we prove that the discrete flow starting from any bounded set of finite fractional perimeter converges exponentially fast to a single ball. As an intermediate result we establish a quantitative Alexandrov type estimate in the fractional setting for normal deformations of a ball. Finally, we provide existence for flat flows as limit points of the discrete flow when the time discretization parameter tends to zero.Mean curvature flowAnisotropic & nonlocal flowsLong-time existence & convergence