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Singularities of Three-Dimensional Ricci Flows

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Ricci Flow and Geometric Applications

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2166))

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Abstract

The Ricci flow is an evolution of a Riemannian metric driven by a parabolic PDEs and was introduced by Hamilton in 1982. It has been the fundamental tool for some important achievements in geometry in the early 2000s, such as Perelman’s proof of the geometrization conjecture and Brendle–Schoen’s proof of the differentiable sphere theorem. In these notes we provide an introduction to the Ricci flow, by giving a survey of the basic results and examples. In particular, we focus our attention on the analysis of the singularities of the flow in the three-dimensional case which is needed in the surgery construction by Hamilton and Perelman.

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Authors and Affiliations

  1. Dip. di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, Via Politecnico 1, 00133, Roma, Italy

    Carlo Sinestrari

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  1. Carlo Sinestrari
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Correspondence to Carlo Sinestrari .

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Editors and Affiliations

  1. Department of Mathematics, University of Pisa, Pisa, Italy

    Riccardo Benedetti

  2. Department of Mathematics, University of Naples, Naples, Italy

    Carlo Mantegazza

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Sinestrari, C. (2016). Singularities of Three-Dimensional Ricci Flows. In: Benedetti, R., Mantegazza, C. (eds) Ricci Flow and Geometric Applications. Lecture Notes in Mathematics(), vol 2166. Springer, Cham. https://doi.org/10.1007/978-3-319-42351-7_3

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