Minkowski problem

In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks for the construction of a strictly convex compact surface S whose Gaussian curvature is specified. More precisely, the input to the problem is a strictly positive real function ƒ defined on a sphere, and the surface that is to be constructed should have Gaussian curvature ƒ(n(x)) at the point x, where n(x) denotes the normal to S at x. Eugenio Calabi stated: "From the geometric view point it [the Minkowski problem] is the Rosetta Stone, from which several related problems can be solved."