  We prove a positive energy theorem in 2+1 dimensional gravity for open
universes and any matter energy-momentum tensor satisfying the dominant energy
condition. We consider on the space-like initial value surface a family of
widening Wilson loops and show that the energy-momentum of the enclosed
subsystem is a future directed time-like vector whose mass is an increasing
function of the loop, until it reaches the value $1/4G$ corresponding to a
deficit angle of $2\pi$. At this point the energy-momentum of the system
evolves, depending on the nature of a zero norm vector appearing in the
evolution equations, either into a time-like vector of a universe which closes
kinematically or into a Gott-like universe whose energy momentum vector, as
first recognized by Deser, Jackiw and 't Hooft is space-like.
  This treatment generalizes results obtained by Carroll, Fahri, Guth and Olum
for a system of point-like spinless particle, to the most general form of
matter whose energy-momentum tensor satisfies the dominant energy condition.
The treatment is also given for the anti de Sitter 2+1 dimensional gravity.
