  In this paper we characterize the intrinsic geometry of apparent horizons
(outermost marginally outer trapped surfaces) in asymptotically flat
spacetimes; that is, the Riemannian metrics on the two sphere which can arise.
Furthermore we determine the minimal ADM mass of a spacetime containing such an
apparent horizon. The results are conveniently formulated in terms of the
quasi-local mass introduced by Bartnik in 1989. The Hawking mass provides a
lower bound for Bartnik's quasilocal mass on apparent horizons by way of
Penrose's conjecture on time symmetric slices, proven in 1997 by Huisken and
Ilmanen and in full generality in 1999 by Bray. We compute Bartnik's mass for
all non-degenerate apparent horizons and show that it coincides with the
Hawking mass. As a corollary we disprove a conjecture due to Gibbons in the
spirit of Thorne's hoop conjecture, and construct a new large class of examples
of apparent horizons with the integral of the negative part of the Gauss
curvature arbitrarily large.
