https://neckpinch.com/authors/anna-kubin/New arXiv papers by Anna Kubin, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2503.05399arxiv:2503.05399Fri, 07 Mar 2025 00:00:00 GMTVedansh Arya, Daniele De Gennaro, Anna Kubin — We study the asymptotic behavior of flat flow solutions to the periodic and planar two-phase Mullins-Sekerka flow and area-preserving curvature flow. We show that flat flows converge to either a finite union of equally sized disjoint disks or to a finite union of disjoint strips or to the complement of these configurations exponentially fast. A key ingredient in our approach is the derivation of a sharp quantitative Alexandrov inequality for periodic smooth sets.Other curvature flowsVolume-preserving & constrained flowsLong-time existence & convergence 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 https://arxiv.org/abs/2201.04174arxiv:2201.04174Tue, 11 Jan 2022 00:00:00 GMTDaniele De Gennaro, Anna Kubin — We show that the discrete approximate volume preserving mean curvature flow in the flat torus T^N starting near a strictly stable critical set E of the perimeter converges in the long time to a translate of E exponentially fast. As an intermediate result we establish a new quantitative estimate of Alexandrov type for periodic strictly stable constant mean curvature hypersurfaces. Finally, in the two dimensional case a complete characterization of the long time behaviour of the discrete flow with arbitrary initial sets of finite perimeter is provided.Mean curvature flowVolume-preserving & constrained flowsSurfacesLong-time existence & convergenceMinimal & CMC surfaces