  Areas of extremal surfaces anchored to sub-regions on screens in Minkowski
space satisfy various entanglement entropy inequalities. In 2+1 dimensions
where the arguments are simplest, we demonstrate (a) monogamy of mutual
information, (b) various versions of (strong) subadditivity, (c) various
inequalities involving the entanglement of purification, as well as (e)
reflection inequality and (f) Araki-Lieb inequality. Just as in AdS,
Linden-Winter and the tower of Cadney-Linden-Winter inequalities are satisfied
trivially. All of these are purely geometric (and therefore unambiguous)
statements, and we expect them to hold semi-classically when $G_N \rightarrow
0$. The results of arXiv:2103.17253 suggest that it is unlikely that there is
non-analyticity at $G_N=0$. These observations have relevance for the Page
phase transition in flat space black holes observed with respect to a screen in
arXiv:2005.02993 and arXiv:2006.06872. In particular, they constitute a
Lorentzian argument that these extremal surface transitions are indeed phase
transitions of $some$ suitably defined entanglement entropy associated to
$subregions$ on the screen.
