  A careful reduction of the three-dimensional gravity to the Liouville
description is performed, where all gauge fixing and on-shell conditions come
from the definition of asymptotic de Sitter spaces. The roles of both past and
future infinities are discussed and the conditions space-time evolution imposes
on both Liouville fields are explicited. Space-times which correspond to
non-equivalent profiles of the Liouville field at past and future infinities
are shown to exist. The qualitative implications of this for any tentative dual
theory are presented.
