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arXiv · 2510.01084

The $L_p$ chord Minkowski problem for super-critical exponent

Shibing Chen·Qi-Rui Li·Yuanyuan Li
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Abstract

The $L_p$ chord Minkowski problem was recently introduced 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. In this paper, we solve the $L_p$ chord Minkowski problem for the super-critical exponents by combining a nonlocal Gauss curvature flow introduced in \cite{HHLW exi} and a topological argument developed in \cite{GLW2022}. Notably, we provide a simplified argument for the topological part.

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Shibing Chen, Qi-Rui Li, Yuanyuan Li. 2025-10-01. The $L_p$ chord Minkowski problem for super-critical exponent. https://arxiv.org/abs/2510.01084

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