https://neckpinch.com/authors/marco-magliaro/New arXiv papers by Marco Magliaro, from Neckpinch Tue, 03 Nov 2026 08:41:12 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