abstract:In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks, for a given strictly positive real function ƒ defined on sphere, for a strictly convex compact surface S whose Gaussian curvature at the point x equals ƒ(n(x)), where n(x) denotes the normal to S at x. Eugenio Calabi stated: "From the geometric view point the Minkowski problem is the Rosetta Stone, from which several related problems can be solved.