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arXiv · 2301.07603

The $L_p$ Chord Minkowski problem in a critical interval

Lujun Guo·Dongmeng Xi·Yiming Zhao
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Abstract

Chord measures and $L_p$ chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric invariants called chord integrals. Prescribing the $L_p$ chord measure is known as the $L_p$ chord Minkowski problem, which includes the $L_p$ Minkowski problem heavily studied in the past 2 decades as special cases. In the current work, we solve the $L_p$ chord Minkowski problem when $0\leq p<1$, without symmetry assumptions.

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Lujun Guo, Dongmeng Xi, Yiming Zhao. 2023-01-18. The $L_p$ Chord Minkowski problem in a critical interval. https://arxiv.org/abs/2301.07603

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