The discrete logarithmic Minkowski problem for the electrostatic $\mathfrak{p}$-capacity

Minhyun Kim; Taehun Lee

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arXiv · 2111.07321

The discrete logarithmic Minkowski problem for the electrostatic $\mathfrak{p}$-capacity

Minhyun Kim·Taehun Lee

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Abstract

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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Minhyun Kim, Taehun Lee. 2021-11-14. The discrete logarithmic Minkowski problem for the electrostatic $\mathfrak{p}$-capacity. https://arxiv.org/abs/2111.07321

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