Stable Capillary Minimal Hypersurfaces in ${\mathbb{R}}_{+}^4$

We prove that a complete, two-sided, stable capillary minimal hypersurface in ${\mathbb{R}}_{+}^4$ is flat provided its contact angle $\theta$ satisfies $\mathrm{\mid }\cot \theta \mathrm{\mid }<{\kappa }_{\ast }$, where ${\kappa }_{\ast }=4\mathrm{\Gamma }(3\mathrm{/}4{)}^2\mathrm{/}\mathrm{\Gamma }(1\mathrm{/}4{)}^2\approx 0.45$.