  We prove uniform finite-time existence of solutions to the vacuum Einstein
equations in polarized U(1) symmetry which have uniformly positive incoming
$H^1$ energy supported on an arbitrarily small set in the 2 + 1 spacetime
obtained by quotienting by the U(1) symmetry. We also construct a subclass of
solutions for which the energy remains concentrated (along a U(1) family of
geodesics) throughout its evolution. These results rely on three innovations: a
direct treatment of the 2 + 1 Einstein equations in a null geodesic gauge, a
novel parabolic scaling of the Einstein equations in this gauge, and a new
Klainerman-Sobolev inequality on rectangular strips.
