Metric Perspectives of the Ricci Flow Applied to Disjoint Unions

Sajjad Lakzian; Michael Munn

Analysis and Geometry in Metric Spaces (2014)

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

Abstract

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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.

How to cite

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Sajjad 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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