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

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

2009-10-31

arxiv.org/abs/0911.0061v1

Journal of Geometry and Physics, Volume 61, Issue 10, October 2011, Pages 1809-1822

Mathematics

Differential Geometry

17 pages, 1 figure

Scientific paper

10.1016/j.geomphys.2011.04.001

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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