  The spatial dependence of the superfluid density is calculated for the
Kosterlitz-Thouless transition in the presence of hard-wall boundaries, for the
case of a single wall bounding the half-infinite plane, and for a superfluid
strip bounded by two walls. The boundaries induce additional vortices that
cause the superfluid density to become anisotropic, with the tensor component
perpendicular to the wall falling to zero at the wall, whereas the component
parallel to the wall remains finite. The effects of the boundaries are found to
extend over all measured length scales, since the correlation length is
infinite in the superfluid phase.
