https://neckpinch.com/authors/bogdan-vasile-matioc/New arXiv papers by Bogdan-Vasile Matioc, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2207.07474/arxiv:2207.07474Fri, 15 Jul 2022 00:00:00 GMTBogdan-Vasile Matioc, Christoph Walker — We establish the well-posedness of the nonlocal mean curvature flow of order α∈(0,1) for periodic graphs on ℝⁿ in all subcritical little Hölder spaces rm h^(1+β)(Tⁿ) with β∈(0,1). Furthermore, we prove that if the solution is initially sufficiently close to its integral mean in rm h^(1+β)(Tⁿ), then it exists globally in time and converges exponentially fast towards a constant. The proofs rely on the reformulation of the equation as a quasilinear evolution problem, which is shown to be of parabolic type by a direct localization approach, and on abstract parabolic theories for such problems.Mean curvature flowAnisotropic & nonlocal flowsLong-time existence & convergence