The Penrose inequality is a mass-area bound for an initial data set containing an outward trapped region. In one asymptotically flat formulation
in spatial dimension 
, data satisfy the dominant
energy condition and the inner boundary is weakly
future outer trapped. The proposed bound is
 |
where 
is invariant ADM mass and 
is the area of the unit
sphere. Here 
is the infimum of areas of full enclosing cuts of the compact inner boundary 
. A cut is the entire intrinsic boundary 
of a connected smooth closed
end-containing domain 
whose interior lies in the open exterior. All its components
and portions coinciding with 
count. Competitors can be disconnected, and the infimum need
not be attained. In spatial dimension 3 the bound is
.
