The General Dual-Polar Orlicz–Minkowski Problem

This paper gives a systematic study to the general dual-polar Orlicz–Minkowski problem (e.g., Problem 4.1). involves dual volume $${\widetilde{V}}_G(\cdot )$$ recently proposed in Gardner et al. (Calc Var PDE 58:35, 2019; 59:33, 2020) order problem. As extends and qth volume, is “polar" initiated “dual" newly polar Luo (Indiana Univ Math J 69:385–420, 2020). The existence, uniqueness continuity, if applicable, for solutions are established. Polytopal and/or counterexamples discrete measures also provided. Several variations of discussed as well, particular one leading Orlicz–Petty bodies.