ricci_flow

`Geometric heat equation`

Ricci flow is a central object in geometric analysis. It is the geometric analogue of the heat equation, used to change the shape of spaces.

It is the main ingredient in Perelman's proof of Thurston's geometrization conjecture, with special case the Poincarè conjecture. For a Riemannian manifold $(M,g)$, the Ricci flow is given by $$\frac{\partial g}{\partial t}=-2\,\mathrm{Ric}(g).$$

A very elementary introduction with nice pictures:

- Gabriel Khan.
*An Illustrated Introduction to the Ricci Flow*, arXiv:2201.04923

- Curvature
- Thurston geometrization
- Poincaré conjecture

ricci_flow.txt · Last modified: 2022/01/14 16:01 by alex_th