  M.Gromov extended the concepts of conformal and quasiconformal mapping to the
mappings acting between the manifolds of different dimensions. For instance,
any entire holomorphic function $ f: \Cn \to {\mathbb C}$ defines a mapping
conformal in the sense of Gromov. In this connection Gromov addressed a natural
question: which facts of the classical theory apply to these mappings? In
particular is it true that
  {\em If the mapping $ F: \R^{n + 1} \to \R^{n}$ is conformal and bounded,
then it is a constant mapping, provided that $ n \geq 2 $}~?
  We present arguments confirming the validity of such a Liouville-type
theorem.
