An isoperimetric constant associated to horizons in S 3 blown up at two points

Let g be a metric on S 3 with positive Yamabe constant. When blowing up g at two points, a scalar flat manifold with two asymptotically flat ends is produced and this manifold will have compact minimal surfaces. We introduce the Θ -invariant for g which is an isoperimetric constant for the cylindric...

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Bibliographic Details
Published in:Journal of geometry and physics 2011-10, Vol.61 (10), p.1809-1822
Main Authors: Dahl, Mattias, Humbert, Emmanuel
Format: Article
Language:English
Subjects:
Asymptotically flat manifolds
Inverse mean curvature flow
Yamabe invariant
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Summary:Let g be a metric on S 3 with positive Yamabe constant. When blowing up g at two points, a scalar flat manifold with two asymptotically flat ends is produced and this manifold will have compact minimal surfaces. We introduce the Θ -invariant for g which is an isoperimetric constant for the cylindrical domain inside the outermost minimal surface of the blown-up metric. Further we find relations between Θ and the Yamabe constant and the existence of horizons in the blown-up metric on R 3 .
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2011.04.001