In three-dimensional Euclidean space, Alexandrov solved the problem of recovering a convex surface from a given extrinsic curvature of the vertices in the class of convex polyhedra and generalized it for the class of convex surfaces. The purpose of this article is to solve an analogue problem in semi-hyperbolic space. First we interpret the semi-hyperbolic space inside the sphere of isotropic space. Let us prove that convex surfaces of semi-hyperbolic space are represented by convex surfaces contained within the sphere of isotropic space. The sphere of isotropic space is a cylinder with rectilinear generatrices. Moreover, bounded convex surfaces in semi-hyperbolic space are expressed by convex surfaces strictly containing inside a sphere of isotropic space, and infinite surfaces using surfaces that have common points with a cylinder, that is, a sphere of isotropic space. For convex surfaces in semi-hyperbolic space, the extrinsic curvature is determined as a positive definite, additive function of the Borel set. A theorem for the existence and uniqueness of a surface with a given function of extrinsic curvature is proven which is equivalent to the existence and uniqueness of a solution to the Monge–Ampere equation.