GEOMETRY OF LOCAL LACUNAE OF HYPERBOLIC OPERATORS WITH CONSTANT-COEFFICIENTS

A graphical geometric characterization is given of local lacunae (doma ins of regularity of the fundamental solution) near the simple singula r 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 po ints on its boundary, and its boundary has no edges of regression near which the component in question is a ''large'' component of the compl ement of the front.