CLC number: O186.16

The Orlicz Minkowski Problem for Logarithmic Capacity

对数容量的Orlicz Minkowski问题

School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 20 November 2024

Abstract

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 $L_p$ 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.

摘要

对数容量的 Orlicz Minkowski 问题旨在确定给定有限 Borel 测度成为凸体的 Orlicz 对数容度测度的充要条件。对数容量的 Minkowski 问题和对数容量的 $L_p$ Minkowski 问题是对数容量的 Orlicz Minkowski 问题的特殊情况。对于离散测度情形的对数容量 Orlicz Minkowski 问题已被解决。在本文中，我们采用逼近法解决了一般 Borel 测度的对数容量 Orlicz Minkowski 问题。