Critical behavior in Ricci flow

Abstract

We use numerical techniques to study the formation of singularities in Ricci flow. Comparing the Ricci flows corresponding to a one parameter family of initial geometries on S^3 with varying amounts of S^2 neck pinching, we find critical behavior at the threshold of singularity formation.

17 pages, 10 figures

References in corpus (1)

• Critical phenomena in gravitational collapse (Physics Reports)

Cited by in corpus (6)

• Ricci solitons, Ricci flow, and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua
• A numerical approach to finding general stationary vacuum black holes
• Numerical Kaehler-Einstein metric on the third del Pezzo
• Geometric flows and (some of) their physical applications
• Critical behavior of collapsing surfaces
• The Ricci flow of the `RP3 geon' and noncompact manifolds with essential minimal spheres