Topological Half-Space Theorems for Minimal Hypersurfaces in $\mathbb{R}^4$

The three-dimensional catenoid in $\mathbb{R}^4$ is a complete embedded minimal hypersurface contained in a slab, showing that the half-space theorem does not extend directly to higher dimensions. We show that this obstruction is topological in $\mathbb{R}^4$. More precisely, we prove that a connect