The discrete logarithmic Minkowski problem for q-capacity

Inverse Gauss Curvature Flows and Orlicz Minkowski Problem

“…The Minkowski type problem for the measure associated with the solution to the boundaryvalue problem is doubtless an extremely important variant, as some typical examples, we refer to seminal papers [9,23] on capacity and torsional rigidity by Jerison and Colesanti-Fimiani and subsequent progress, e.g., [4,10,12,21,37,39,40].…”

“…Feng et al [12] supplemented the case of p ∈ (0, 1) and p ∈ (1, n) for general measures. When p = 0 and p ∈ (1, n) in (1.6), it is the logarithmic Minkowski problem for p-capacity, and its polytopal solution is proved in [37].…”