Anoumou Attiogbe — Neckpinchhttps://neckpinch.com/authors/anoumou-attiogbe/New arXiv papers by Anoumou Attiogbe, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Short time existence and smoothness of the nonlocal mean curvature flow of graphshttps://neckpinch.com/papers/2205.01248/arxiv:2205.01248Mon, 02 May 2022 00:00:00 GMTAnoumou Attiogbe, Mouahmed Moustapha Fall, Tobias Weth — We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. For this, we study the associated nonlocal quasilinear evolution equation satisfied by the family of graph functions. We establish, using an analytic semigroup approach, short time existence, uniqueness and optimal Hölder regularity in time and space of classical solutions of the nonlocal equation, depending on the regularity of the initial graph. The method also yields C^∞-smoothness estimates of the evolving graphs for positive times.Mean curvature flowAnisotropic & nonlocal flowsStability & uniquenessHarmonic maps & DeTurck trick