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arXiv · 0911.0061

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

Mattias Dahl·Emmanuel Humbert
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Abstract

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 $\Th$-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 $\Th$ and the Yamabe constant and the existence of horizons in the blown-up metric on $\mR^3$.

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Mattias Dahl, Emmanuel Humbert. 2009-10-31. An isoperimetric constant associated to horizons in $S^3$ blown-up at two points. https://doi.org/10.1016/j.geomphys.2011.04.001

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