The Orlicz-Minkowski problem for polytopes
The classical Minkowski problem and various modern versions of it, known as Minkowski-type problems, are crucial in the study of convex bodies throughout the 20th and 21st century and even more so in the last few decades. Some of the most influential Minkowski-type problems include the \(L_p\) Minkowski problem (which contains the well-known logarithmic Minkowski problem) and the recently posed dual Minkowski problems. These problems, with enough regularity assumed, reduce to the study of a family of Monge-Ampere type equations. The uniqueness of these solutions are often tied to isoperimetric inequalities and spetrum analysis of certain second order nonlinear elliptic operators. The current paper establishes some existence result for the Orlicz Minkowski problem. It uses a variational approach and studies particularly the discrete case.
scientific article; zbMATH DE number 7440390
scientific article