The Orlicz-Gauss image problem for pseudo-cones and its associated spherical optimal transport

Pseudo-cones serve as the noncompact counterpart of convex bodies in convex geometry. This paper establishes a necessary and sufficient condition for the existence of solutions to the Orlicz-Gauss image problem for pseudo-cones and further demonstrates its connection to spherical optimal transport. Our approach combines the variational method with a novel restrictive technique, thereby strengthening the original result of Schneider up to a constant factor.