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- W4312909045 abstract "The Ricci flow is a natural evolution equation for Riemannian metrics on a given manifold. The main goal is to understand singularity formation. In his spectacular 2002 breakthrough, Perelman achieved a qualitative understanding of singularity formation in dimension 3. More precisely, Perelman showed that every finite-time singularity to the Ricci flow in dimension 3 is modeled on an ancient $$kappa $$ -solution. Moreover, Perelman proved a structure theorem for ancient $$kappa $$ -solutions in dimension 3. In this survey, we discuss recent developments which have led to a complete classification of all the singularity models in dimension 3. Moreover, we give an alternative proof of the classification of noncollapsed steady gradient Ricci solitons in dimension 3 (originally proved by the author in 2012)." @default.
- W4312909045 created "2023-01-05" @default.
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- W4312909045 date "2022-01-01" @default.
- W4312909045 modified "2023-09-30" @default.
- W4312909045 title "Singularity Models in the Three-Dimensional Ricci Flow" @default.
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- W4312909045 doi "https://doi.org/10.1007/978-981-19-3708-8_3" @default.
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