# Metric Perspectives of the Ricci Flow Applied to Disjoint Unions

Analysis and Geometry in Metric Spaces (2014)

- Volume: 2, Issue: 1, page 282-293, electronic only
- ISSN: 2299-3274

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topSajjad Lakzian, and Michael Munn. "Metric Perspectives of the Ricci Flow Applied to Disjoint Unions." Analysis and Geometry in Metric Spaces 2.1 (2014): 282-293, electronic only. <http://eudml.org/doc/268689>.

@article{SajjadLakzian2014,

abstract = {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.},

author = {Sajjad Lakzian, Michael Munn},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {super Ricci flow; disjoint union; heat kernel},

language = {eng},

number = {1},

pages = {282-293, electronic only},

title = {Metric Perspectives of the Ricci Flow Applied to Disjoint Unions},

url = {http://eudml.org/doc/268689},

volume = {2},

year = {2014},

}

TY - JOUR

AU - Sajjad Lakzian

AU - Michael Munn

TI - Metric Perspectives of the Ricci Flow Applied to Disjoint Unions

JO - Analysis and Geometry in Metric Spaces

PY - 2014

VL - 2

IS - 1

SP - 282

EP - 293, electronic only

AB - 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.

LA - eng

KW - super Ricci flow; disjoint union; heat kernel

UR - http://eudml.org/doc/268689

ER -

## References

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