https://neckpinch.com/authors/fernanda-roing/New arXiv papers by Fernanda Roing, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2502.09199/arxiv:2502.09199Thu, 13 Feb 2025 00:00:00 GMTMarco Magliaro, Luciano Mari, Fernanda Roing, Andreas Savas-Halilaj — In this paper, we consider soliton solutions of the mean curvature flow in the unit sphere S²ⁿ⁺¹ moving along the integral curves of the Hopf unit vector field. While such solitons must necessarily be minimal if compact, we produce a non-minimal, complete example with topology S²ⁿ⁻¹ × R. The example wraps around a Clifford torus S²ⁿ⁻¹ × S¹ along each end, it has reflection and rotational symmetry and its mean curvature changes sign on each end. Indeed, we prove that a complete 2-dimensional soliton with non-negative mean curvature outside a compact set must be a covering of a Clifford torus. Concluding, we obtain a pinching theorem under suitable conditions on the second fundamental form.Mean curvature flowCurvature pinchingSurfacesRotational symmetry & warped products https://neckpinch.com/papers/2202.04158/arxiv:2202.04158Tue, 08 Feb 2022 00:00:00 GMTJorge Lira, Fernanda Roing — We prove the longtime existence for the mean curvature flow problem with a perpendicular Neumann boundary condition in a Generalized Robertson Walker (GRW) spacetime that obeys the null convergence condition. In addition, we prove that the metric of such a solution is conformal to the one of the leaf of the GRW in asymptotic time. Furthermore, if the initial hypersurface is mean convex, then the evolving hypersurfaces remain mean convex during the flow.Mean curvature flowBoundaries & non-compactFree boundary & capillaryLong-time existence & convergence