Stable Free Boundary Minimal Hypersurfaces in ${\mathbb{B}}^5$ and ${\mathbb{B}}^6$

Abstract

In this paper, we prove that there is no complete two-sided stable immersed free boundary minimal hypersurface in the closed Euclidean unit ball ${\mathbb{B}}^{n+1}$ for $n\le 5$.

32 pages, comments welcome!