https://neckpinch.com/authors/abdelmouksit-sagueni/New arXiv papers by Abdelmouksit Sagueni, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2510.00746arxiv:2510.00746Wed, 01 Oct 2025 00:00:00 GMTBlanche Buet, Gian Paolo Leonardi, Simon Masnou, Abdelmouksit Sagueni — We propose a construction of mean curvature flows by approximation for very general initial data, in the spirit of the works of Brakke and of Kim & Tonegawa based on the theory of varifolds. Given a general varifold, we construct by iterated push-forwards an approximate time-discrete mean curvature flow depending on both a given time step and an approximation parameter. We show that, as the time step tends to 0, this time-discrete flow converges to a unique limit flow, which we call the approximate mean curvature flow. An interesting feature of our approach is its generality, as it provides an approximate notion of mean curvature flow for very general structures of any dimension and codimension, ranging from continuous surfaces to discrete point clouds. We prove that our approximate mean curvature flow satisfies several properties: stability, uniqueness, Brakke-type equality, mass decay. By coupling this approximate flow with the canonical time measure, we prove convergence, as the approximation parameter tends to 0, to a spacetime limit measure whose generalized mean curvature is bounded. Under an additional rectifiability assumption, we further prove that this limit measure is a spacetime Brakke flow.Mean curvature flowWeak & singular flowsStability & uniqueness https://arxiv.org/abs/2509.06441arxiv:2509.06441Mon, 08 Sep 2025 00:00:00 GMTAbdelmouksit Sagueni — We prove that the spacetime Brakke flow constructed by Buet et al. is non-trivial as long as the initial varifold is a union of boundaries of domains of finite perimeter. In the codimension 1 setting, we show that, starting from a smooth boundary, the support of the mass measure of the spacetime Brakke flow coincides with the support of the classical mean curvature flow.Mean curvature flowWeak & singular flows https://arxiv.org/abs/2509.06440arxiv:2509.06440Mon, 08 Sep 2025 00:00:00 GMTAbdelmouksit Sagueni — In this paper we aim to study the consistency of the mean curvature flow via discretization. We will use discretizations by volumetric varifolds, and derive a Brakke approximate equality involving the masses of the volumetric varifolds and their approximate mean curvatures.Mean curvature flowWeak & singular flows