Abstract

Given a domain $\Omega $ of $\mathbb{R}^{m+1}$ and a $k$-dimensional non-degenerate minimal submanifold $K$ of $\partial \Omega $ with $1\le k\le m-1$, we prove the existence of a family of embedded constant mean curvature hypersurfaces in $\Omega $ which as their mean curvature tends to infinity concentrate along $K$ and intersecting $\partial \Omega $ perpendicularly along their boundaries