Geodesic
Metric Perspectives of the Ricci Flow Applied to Disjoint Unions
Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1.

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In this paper we consider compact, Riemannian manifolds M1, M2 each equipped with a oneparameter family of metrics g1(t), g2(t) satisfying the Ricci flow equation. Adopting the characterization of super-solutions to the Ricci flow developed by McCann-Topping, we define a super Ricci flow for a family of distance metrics defined on the disjoint union M1 ⊔ M2. In particular, we show such a super Ricci flow property holds provided the distance function between points in M1 and M2 is itself a super solution of the heat equation on M1 × M2. We also discuss possible applications and examples.
Mots-clés : super Ricci flow, disjoint union, heat kernel 
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Lakzian, Sajjad; Munn, Michael. Metric Perspectives of the Ricci Flow Applied to Disjoint Unions. Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a4/