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

Song, Antoine¹

¹ Department of Mathematics, Princeton University, Princeton, NJ, United States

Geometry & topology, Tome 23 (2019) no. 7, pp. 3501-3535.

Résumé

We construct spherical space forms $\left(S^3∕\Gamma ,g\right)$ with positive scalar curvature and containing no stable embedded minimal surfaces such that the following happens along the Ricci flow starting at $\left(S^3∕\Gamma ,g\right)$: a stable embedded minimal $2$–sphere appears and a nontrivial singularity occurs. We also give in dimension $3$ a general construction of Type I neckpinching and clarify the relationship between stable spheres and nontrivial 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.

Détail

DOI : 10.2140/gt.2019.23.3501

Classification : 53A10, 53C44
Keywords: Ricci flow, minimal spheres, scalar curvature

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