https://neckpinch.com/authors/laurent-mazet/New arXiv papers by Laurent Mazet, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2010.01994/arxiv:2010.01994Mon, 05 Oct 2020 00:00:00 GMTLaurent Mazet — In this paper, we prove that a Riemannian n-manifold M with sectional curvature bounded above by 1 that contains a minimal 2-sphere of area 4π which has index at least n-2 has constant sectional curvature 1. The proof uses the construction of ancient mean curvature flows that flow out of a minimal submanifold. As a consequence we also prove a rigidity result for the Simon-Smith minimal spheres.Mean curvature flowAncient solutionsStability & uniquenessMinimal & CMC surfaces