https://neckpinch.com/authors/vanderson-lima/New arXiv papers by Vanderson Lima, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2105.07504/arxiv:2105.07504Sun, 16 May 2021 00:00:00 GMTMarco A. M. Guaraco, Vanderson Lima, Franco Vargas Pallete — We study global aspects of the mean curvature flow of non-separating hypersurfaces S in closed manifolds. For instance, if S has non-vanishing mean curvature, we show its level set flow converges smoothly towards an embedded minimal hypersurface Γ. We prove a similar result for the flow with surgery in dimension 2. As an application we show the existence of monotone incompressible isotopies in manifolds with negative curvature. Combining this result with min-max theory, we show that quasi-Fuchsian and hyperbolic 3-manifolds fibered over S¹ admit smooth entire foliations whose leaves are either minimal or have non-vanishing mean curvature. We also conclude the existence of outermost minimal surfaces for quasi-Fuchsian ends and study their continuity with respect to variations of the quasi-Fuchsian metric.Mean curvature flowSurgeryWeak & singular flowsLong-time existence & convergenceMinimal & CMC surfaces