This result states existence of mass-minimizing integral currents with prescribed boundary and compact support: given U R n be open, let 1 m n, let I m-1 (U) be an integral (m-1)-current satisfying = 0, and let K U be compact. Define A ,K (U) := \ R I m(U) : R = ,\ spt R K\ . Assume that A.... It is useful in geometric measure theory and minimal surface regularity, where variational identities, curvature estimates, and compactness arguments control geometric objects.