https://neckpinch.com/authors/antonin-chambolle/New arXiv papers by Antonin Chambolle, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2506.05946arxiv:2506.05946Fri, 06 Jun 2025 00:00:00 GMTAntonin Chambolle, Daniele De Gennaro, Massimiliano Morini — We consider a fully discrete and explicit scheme for the mean curvature flow of boundaries, based on an elementary diffusion step and a precise redistancing operation. We give an elementary convergence proof for the scheme under the standard CFL condition h∼e², where h is the time discretization step and e the space step. We discuss extensions to more general convolution/redistancing schemes.Mean curvature flow https://arxiv.org/abs/2403.04725arxiv:2403.04725Thu, 07 Mar 2024 00:00:00 GMTAntonin Chambolle, Daniele De Gennaro, Massimiliano Morini — We consider here a fully discrete variant of the implicit variational scheme for mean curvature flow [AlmTayWan,LucStu], in a setting where the flow is governed by a crystalline surface tension defined by the limit of pairwise interactions energy on the discrete grid. The algorithm is based on a new discrete distance from the evolving sets, which prevents the occurrence of the spatial drift and pinning phenomena identified in [MisiatsYip16,BraGelNov] in a similar discrete framework. We provide the first rigorous convergence result holding in any dimension, for any initial set and for a large class of purely crystalline anisotropies, in which the spatial discretization mesh can be of the same order or coarser than the time step.Mean curvature flowOther curvature flowsAnisotropic & nonlocal flows https://arxiv.org/abs/2212.05027arxiv:2212.05027Fri, 09 Dec 2022 00:00:00 GMTAntonin Chambolle, Daniele De Gennaro, Massimiliano Morini — In this paper we address anisotropic and inhomogeneous mean curvature flows with forcing and mobility, and show that the minimizing movements scheme converges to level set/viscosity solutions and to distributional solutions à la Luckhaus-Sturzenhecker to such flows, the latter holding in low dimension and conditionally to a convergence of the energies. By doing so we generalize recent works concerning the evolution by mean curvature by removing the hypothesis of translation invariance, which in the classical theory allows to simplify many arguments.Mean curvature flowWeak & singular flowsHomogeneous spaces