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arXiv · 2304.11299

The $Lp$ chord Minkowski problem for negative $p$

Yuanyuan Li
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Abstract

In this paper, we solve the $L_p$ chord Minkowski problem in the case of discrete measures whose supports are in general position for negative $p$ and $q>0.$ As for general Borel measure with a density, we also give a proof but need $p\in(-n,0)$ and $n+1>q\geqslant 1.$ The $L_p$ chord Minkowski problem was recently posed by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the $L_p$ chord measure of a convex body, and it includes the chord Minkowski problem and the $L_p$ Minkowski problem.

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Yuanyuan Li. 2023-04-22. The $Lp$ chord Minkowski problem for negative $p$. https://arxiv.org/abs/2304.11299

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