Research profile

Antoine Song

Works on curvature pinching, minimal & CMC surfaces and sphere theorems.

NP-RC-828953

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  • Published in Geometry & Topology

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Curvature pinchingMinimal & CMC surfacesSphere theoremsScalar curvatureSingularitiesRicci flow

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Papers

Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2016

math.DGv2arXiv:1611.09747

Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature

Antoine Song

We construct examples of spherical space forms with positive scalar curvature and containing no stable embedded minimal surfaces, such that the following happens along the Ricci flow starting at : a stable embedded minimal two-sphere appears and a non-trivial singularity occurs. We also give in dimension 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
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NP-RC-828953 is Antoine Song's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.

A window on one part of a person's work: papers here go back to 2016 and cover Ricci flow and its neighbouring flows, with the older work the site recommends, so this page is no measure of anyone's whole output. Being listed is not an endorsement by or of the person. If two people share this name, their work may appear together here. How it is put together.