Robustness and uniqueness of equilibrium states for certain partially hyperbolic systems

We prove that if $f$ is a $C^{1+}$ partially hyperbolic diffeomorphism satisfying certain conditions then there is a $C^1$-open neighborhood $\text{cA}$ of $f$ so that every $g\in \text{cA}\cap {\mathrm{Diff}}^{1+}(M)$ has a unique equilibrium state.