Geometry of local lacunae of hyperbolic operators with constant coefficients

A graphical geometric characterization is given of local lacunae (domains of regularity of the fundamental solution) near the simple singular points of the wave fronts of nondegenerate hyperbolic operators. To wit: a local (near a simple singularity of the front) component of the complement of the front is a local lacuna precisely when it satisfies the Davydov–Borovikov signature condition near all the nonsingular points on its boundary, and its boundary has no edges of regression near which the component in question is a “large” component of the complement of the front.