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 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 .
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