Christoffel–Minkowski problem for S' (n−2)-nd area measure in general dimensions

Solve the Minkowski problem for the (n−2)-nd area measure S'(K,·) of a convex body in R^n by determining necessary and sufficient conditions on a finite Borel measure μ on S^{n−1} that guarantee the existence of a convex body K with S'(K,·) = μ, in dimensions n > 3.

Background

The Christoffel–Minkowski family of problems prescribes higher-order area measures of convex bodies. While the classical (n−1)-st area measure (surface area measure) case is fully solved, the next case S'(K,·) is open in general, except for some regular settings.

In relating their new chord measures to classical objects, the authors emphasize that the q = 0 limit touches the still unresolved Christoffel–Minkowski case for S'.