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.
@article{bwmeta1.element.doi-10_2478_agms-2014-0011,
author = {Sajjad Lakzian and Michael Munn},
title = {Metric Perspectives of the Ricci Flow Applied to Disjoint Unions},
journal = {Analysis and Geometry in Metric Spaces},
volume = {2},
year = {2014},
zbl = {1322.53037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_agms-2014-0011}
}
Sajjad Lakzian; Michael Munn. Metric Perspectives of the Ricci Flow Applied to Disjoint Unions. Analysis and Geometry in Metric Spaces, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_agms-2014-0011/
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