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

Song, Antoine (2019) Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature. Geometry & Topology, 23 (7). pp. 3501-3535. ISSN 1364-0380. doi:10.2140/gt.2019.23.3501.

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We construct 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 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.

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Additional Information:I am grateful to my advisor Fernando Codá Marques for his support and his helpful remarks. I also thank Ian Agol for sharing his former thoughts about these questions related to the study of singularities, and Otis Chodosh, John Lott and Richard Bamler for their interest. The author was supported by NSF-DMS-1509027.
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Issue or Number:7
Record Number:CaltechAUTHORS:20221026-539155000.13
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117600
Deposited By: George Porter
Deposited On:26 Oct 2022 22:22
Last Modified:26 Oct 2022 22:22

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