Outer area-minimizing surface
= Outer area-minimizing surface
An <outer area-minimizing surface> is a closed surface in a Riemannian initial-data slice whose area is no greater than that of any enclosing competitor. This is a variational property, not a consequence of containment alone. It is important when choosing the horizon-area quantity in the <Riemannian Penrose inequality> and when examining an <apparent-horizon area comparison>.