Horizons in noncompact fill-ins of nonnegative scalar curvature

Abstract Given a complete Riemannian metric of nonnegative scalar curvature on $$\Sigma \times (-\infty , 0 ] $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Σ</mml:mi> <mml:mo>×</mml:mo> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> , where $$\Sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Σ</mml:mi> </mml:math> denotes a 2-sphere, we exhibit conditions that imply the existence of a closed minimal surface homologous to the boundary.