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 threedimensional case which is needed in the surgery construction by Hamilton and Perelman.

Sinestrari, C. (2016). Singularities of three-dimensional Ricci flows. In Ricci flow and geometric applications (pp. 71-104). Springer Verlag [10.1007/978-3-319-42351-7_3].

Singularities of three-dimensional Ricci flows

SINESTRARI, CARLO
2016

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 threedimensional case which is needed in the surgery construction by Hamilton and Perelman.
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
English
Rilevanza internazionale
Capitolo o saggio
http://www.springer.com/series/304
Sinestrari, C. (2016). Singularities of three-dimensional Ricci flows. In Ricci flow and geometric applications (pp. 71-104). Springer Verlag [10.1007/978-3-319-42351-7_3].
Sinestrari, C
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/179605
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