  We give the solution of the Monge-Kantorovitch problem on the Wiener space
for the singular Wasserstein metric which is defined with respect to the
distance of the underlying Cameron-Martin space. We show, under the hypothesis
that this distance is finite, the existence and the uniquness of the solutions,
that they are supported by the graphs of the weak derivatives of H-convex
Wiener functionals. then we prove the more general situation, where the
measures are not even necessarily absolutely continuous w.r.to the Wiener
measure. We give sufficient conditions for the hypothesis about the Wassestein
distance is finite with the help of the Girsanov theorem. Finally we give the
solutions of the Monge-Ampere equation using the classical Jacobi
representation and/or the Ito parametrization of the Wiener space.
