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

Abstract

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

arXiv comment25 pages