静电$\mathfrak{p}$ -电容的离散对数Minkowski问题
The discrete logarithmic Minkowski problem for the electrostatic $\mathfrak{p}$-capacity
摘要：
静电容量的闵可夫斯基问题描述了静电容量产生的度量，这是闵可夫斯基问题的一个著名变体。本文将此问题推广为具有$\mathfrak{p}$ -容量的$L_p$ Minkowski问题.特别地，对数情况$p=0$涉及锥体积，因此具有几何意义。本文在给定测度的支撑在一般位置的情况下，解决了离散对数Minkowski问题（$1<\mathfrak{p}<n$）.
英文摘要：
The Minkowski problem for electrostatic capacity characterizes measures generated by electrostatic capacity, which is a well-known variant of the Minkowski problem. This problem has been generalized to $L_p$ Minkowski problem for $\mathfrak{p}$-capacity. In particular, the logarithmic case $p=0$ relates to cone-volumes and therefore has a geometric significance. In this paper we solve the discrete logarithmic Minkowski problem for $1<\mathfrak{p}<n$ in the case where the support of the given measure is in general position.
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