Absolute maximum principle for tight forms

Let $F$ be a tight form and let $U$ be an open set such that

$$H_{d-1}(U,\mathbf{R})=0.$$

Absolute maximum principle for tight forms. The restriction of $|F|$ to $\overline{U}$ attains its maximum on $\partial U$. This would extend the absolute-minimization theorem from sufficiently regular tight forms to arbitrary tight forms; the authors state that they cannot prove it because they lack a maximum principle.