REGULAR DOMAINS AND SURFACES OF CONSTANT GAUSSIAN CURVATURE IN 3-DIMENSIONAL AFFINE SPACE

Generalizing the notion of domains of dependence in the Minkowski space, we define and study regular domains in the affine space with respect to a proper convex cone. In three dimensions, we show that every proper regular domain is uniquely foliated by some particular surfaces with constant affine Gaussian curvature. The result is based on the analysis of a Monge-Ampere equation with extended real-valued lower semicontinuous boundary condition.