  The dimension of cycles in the Tits boundary of a proper Hadamard space is
bounded by the asymptotic rank m of the space minus one. Kleiner and Lang
proved that for (m-1)-dimensional cycles in the Tits boundary, the asymptotic
Plateau problem can be solved. We prove that the asymptotic Plateau problem can
be solved for so called strongly immovable cycles in the Tits boundary of a
proper Hadamard space. The class of strongly immovable cycles contains all
(m-1)-cycles. Further, it is a result of Huang, Kleiner and Stadler that the
class of strongly immovable cycles contains the boundaries of cocompact flats
which do not bound flat half-spaces and we prove that the class of strongly
immovable cycles of a fixed dimension forms a group so our result applies to
new examples.
