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Metric Perspectives of the Ricci Flow Applied to Disjoint Unions

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Lakzian S., Munn M.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

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.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Lakzian S.

1 Munn M.

1 2014

Wyniki wyszukiwania

Metric Perspectives of the Ricci Flow Applied to Disjoint Unions