 Let $\Omega \subset \mathbb{R}^0$ be an open convex set. Let the anisotropy be given by the function $\phi(x,Du) = \| Du \|_p$, where $0 < p < \infty$. Let $E$ be a $\phi-$minimal set with respect to $\Omega$, i.e. $\chi_E$ is a function of $\phi-$least gradient in $\Omega$. Then every connected component of $\partial E$ is a line segment.  