  Various transformations of isothermic surfaces are discussed and their
interrelations are analyzed. Applications to cmc-1 surfaces in hyperbolic space
and their minimal cousins in Euclidean space are presented: the Umehara-Yamada
perturbation, the classical and Bryant's Weierstrass type representations, and
the duality for cmc-1 surfaces are interpreted in terms of transformations of
isothermic surfaces. A new Weierstrass type representation is introduced and a
Moebius geometric characterization of cmc-1 surfaces in hyperbolic space and
minimal surfaces in Euclidean space is given.
