On the combinatorics of Demoulin transforms and (discrete) projective minimal surfaces (Q512265)

The authors show that the classical Demoulin transformation for a projective minimal surface generates a \(\mathbb Z^2\) lattice of projective minimal surfaces generically which they call a Demoulin lattice. Discussing geometric properties of Demoulin lattices, they introduce the notion of lattice Lie quadrics, associated discrete envelopes and the definition of discrete PMQ-surfaces which are discretizations of either projective minimal surfaces or so-called Q-surfaces. They also prove that the even and odd Demoulin sublattices encode a two-parameter family of pairs of discrete PMQ-surfaces with the property that one discrete PMQ-surface constitutes an envelope of the lattice Lie quadrics associated with the other.