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
2016-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
