  Critical collapse of a self-gravitating scalar field in a (2+1)-dimensional
spacetime with negative cosmological constant seems to be dominated by a
continuously self-similar solution of the field equations without cosmological
constant. However, previous studies of linear perturbations in this background
were inconclusive. We extend the continuously self-similar solutions to
solutions of the field equations with negative cosmological constant, and
analyse their linear perturbations. The extended solutions are characterized by
a continuous parameter. A suitable choice of this parameter seems to improve
the agreement with the numerical results. We also study the dynamics of the
apparent horizon in the extended background.
