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arXiv · 1211.2792

Super Ricci flow for disjoint unions

Sajjad Lakzian·Michael Munn
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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.

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Sajjad Lakzian, Michael Munn. 2012-11-12. Super Ricci flow for disjoint unions. https://arxiv.org/abs/1211.2792

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