Stable free boundary minimal hypersurfaces in locally wedge-shaped manifolds

Abstract

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

Update the introduction and add some details on preliminaries and in Section 5. Comments are welcome