The Orlicz Minkowski Problem for Logarithmic Capacity

The Orlicz Minkowski problem for logarithmic capacity seeks to determine the necessary and sufficient conditions for a given finite Borel measure, such that it is the Orlicz logarithmic capacitary measure of a convex body. The Orlicz Minkowski problem for logarithmic capacity includes the Minkowski problem for logarithmic capacity and the Lp Minkowski problem for logarithmic capacity as special cases. The discrete case has been solved by the researchers. In this paper, we solve the Orlicz Minkowski problem for logarithmic capacity with respect to general Borel measures by applying an approximation scheme.