Super Ricci flow for disjoint unions

Abstract

In this paper we consider compact, Riemannian manifolds $M_1,M_2$ each equipped with a one-parameter family of metrics $g_1(t),g_2(t)$ satisfying the Ricci flow equation. Motivated by a characterization of the super Ricci flow developed by McCann-Topping, we introduce the notion of a super Ricci flow for a family of distance metrics defined on the disjoint union $\MM$. In particular, we show such a super Ricci flow property holds provided the distance function between points in $M_1$ and $M_2$ evolves by the heat equation. We also discuss possible applications and examples.

arXiv comment15 pages

Cited by in corpus (2)

• Heat Flows on Time-dependent Metric Measure Spaces and Super-Ricci Flows
• On the Size of a Ricci Flow Neckpinch via Optimal Transport