  Let $f$ be a $C^2$ partially hyperbolic diffeomorphisms of ${\mathbb T}^3$
(not necessarily volume preserving or transitive) isotopic to a linear Anosov
diffeomorphism $A$ with eigenvalues $$\lambda_{s}<1<\lambda_{c}<\lambda_{u}.$$
Under the assumption that the set $$\{x: \,\mid\log
\det(Tf\mid_{E^{cu}(x)})\mid \leq \log \lambda_{u} \}$$ has zero volume inside
any unstable leaf of $f$ where $E^{cu} = E^c\oplus E^u$ is the center unstable
bundle, we prove that the stable foliation of $f$ is $C^1$ robustly minimal,
i.e., the stable foliation of any diffeomorphism $C^1$ sufficiently close to
$f$ is minimal. In particular, $f$ is robustly transitive.\par
  We build, with this criterion, a new example of a $C^1$ open set of partially
hyperbolic diffeomorphisms, for which the strong stable foliation and the
strong unstable foliation are both minimal.
