The Gauss Image Problem

The Hadwiger theorem on convex functions. II

“…The Hadwiger theorem is the first culmination of the program, initiated by Blaschke, of classifying valuations invariant under various groups and the starting point of geometric valuation theory (see [38,Chapter 6]). We refer to [1, 2, 4-6, 18, 19, 25, 27, 30, 31] for some recent classification results and to [7,21,26] for some of the new valuations that keep arising.…”

The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures

“…We remark that the classification of valuations on convex bodies is a classical subject, which is described in [43,Chapter 6]. Also see [10,26] for some newly defined valuations and [2,3,5,7,8,23,24,30,31,34,35] for some recent classification results.…”

A flow approach to the Musielak-Orlicz-Gauss image problem

“…al. [6] is the Gauss image problem, which links two given Borel measures λ and µ on S n via the radial Gauss image α Ω of a convex body Ω. It asks: under what conditions on λ and µ, does there exist a convex body Ω such that µ = λ(α Ω (•))?…”