Optimal transport and Perelman's reduced volume

Abstract

We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.

final version

Cited by in corpus (2)

• Perelman's reduced volume and a gap theorem for the Ricci flow
• Optimal transportation and monotonic quantities on evolving manifolds