Stable free boundary minimal hypersurfaces in locally wedge-shaped manifolds

We prove that a stable $C^{1,1}$-to-edge properly embedded free boundary minimal hypersurface ${\mathrm{\Sigma }}^3$ of a $4$-dimensional wedge domain ${\mathrm{\Omega }}_{\theta }^4$ with angle $\theta \in (0,\pi ]$ is flat.