Ricci flow

*Ricci flow* is the gradient flow of the the action functional of dilaton gravity: the Einstein-Hilbert action coupled to a dilaton field.

(Equivalently: it is the renormalization group flow of the string sigma-model for background fields containing gravity and dilaton.)

From Rubinstein-Sinclair:

The identification of Ricci flow as a gradient flow of gravity+dilaton is due to

- Perelman,

and was a key step in his completion of Hamilton’s program for how to prove the Poincare conjecture.

A quick survey is in the slides

- Annibale Magni,
*Perelman’s dilaton*(pdf).

A detailed survey is in

Revised on November 19, 2013 11:59:32
by Urs Schreiber
(77.251.114.72)