Bianchi-convex sets and a new maximum principle for the Ricci flow

Abstract

We introduce the new notion of Bianchi-convex sets, a generalization of convex sets of algebraic curvature tensors inspired by the second Bianchi identity. It turns out that Hamilton's maximum principle for the Ricci flow can be generalized for Bianchi-convex sets.

20 pages, 1 figure

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds