https://neckpinch.com/authors/antoine-song/New arXiv papers by Antoine Song, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1611.09747/arxiv:1611.09747Tue, 29 Nov 2016 00:00:00 GMTAntoine Song — We construct examples of spherical space forms (S³/Γ,g) with positive scalar curvature and containing no stable embedded minimal surfaces, such that the following happens along the Ricci flow starting at (S³/Γ,g): a stable embedded minimal two-sphere appears and a non-trivial singularity occurs. We also give in dimension 3 a general contruction of Type I neckpinching and clarify the relationship between stable spheres and non-trivial Type I singularities of the Ricci flow. Some symmetry assumptions prevent the appearance of stable spheres, and this has consequences on the types of singularities which can occur for metrics with these symmetries.Ricci flowSingularitiesCurvature pinchingSphere theoremsScalar curvatureMinimal & CMC surfaces