22 December 2006
Vol 314, Issue 5807

About The Cover

Cover image expansion

COVER To prove the Poincaré Conjecture, Grigori Perelman used the equations for Ricci flow--a procedure for transforming irregular spaces into uniform ones. In this two-dimensional example, the equations prescribe that negatively curved regions (blue) must expand while positively curved regions (red) contract. Over time, the original dumbbell-shaped surface evolves into a sphere. See the Breakthrough of the Year special section beginning on page 1848. Image: Cameron Slayden/, based on data provided by Robert Sinclair