  It is well known that in compact local Lipschitz neighborhood retracts in
Euclidean space flat convergence for integer rectifiable currents amounts just
to weak convergence. In the present paper we extend this result to integral
currents in complete metric spaces admitting a local cone type inequality.
These include in particular all Banach spaces as well as complete CAT(k)-spaces
(metric spaces of curvature bounded above by k in the sense of Alexandrov). The
main result can be used to prove the existence of minimal elements in a fixed
Lipschitz homology class in compact metric spaces admitting local cone type
inequalities or to conclude that integral currents which are weak limits of
sequences of absolutely area minimizing integral currents are again absolutely
area minimizing.
