Cannon–Thurston maps for $${{\,\textrm{CAT}\,}}(0)$$ groups with isolated flats

Abstract Mahan Mitra (Mj) proved Cannon–Thurston maps exist for normal hyperbolic subgroups of a group (Mitra in Topology, 37(3):527–538, 1998). We prove that do not infinite non-hyperbolic $${{\,\textrm{CAT}\,}}(0)$$ CAT ( 0 ) groups with isolated flats respect to the visual boundaries. also show infinite-index flats. obtain structure theorem these settings and outer automorphism have no purely atoroidal $$\mathbb {Z}^2$$ Z 2 subgroups.