A Vertex-Skipping property for almost-minimizers of the relative perimeter in convex sets

Gian Paolo Leonardi, Giacomo Vianello

Given a convex domain $\hat{I}\text{c◯}\subset {\mathbb{R}}^3$ and an almost-minimizer $E$ of the relative perimeter in $\hat{I}\text{c◯}$, we prove that the closure of $\partial E\cap \hat{I}\text{c◯}$ does not contain v…