A new framework of zero mean curvature surfaces in the isotropic 3-space

We introduce a class of zero mean curvature surfaces with singularities in the isotropic 3-space, called ZMC-faces. As a main result, we establish three Osserman-type inequalities for a ZMC-face under certain assumptions on both completeness and finiteness of the total curvature. The equality conditions of these inequalities are related to the asymptotic behaviors of the ends. Moreover, we present several examples of ZMC-faces attaining equalities in these inequalities.