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The $L_p$ Chord Minkowski problem in a critical interval

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arxiv 2301.07603 v2 pith:XYHMO34E submitted 2023-01-18 math.MG math.CA

Lujun Guo , Dongmeng Xi , Yiming Zhao This is my paper · ORCID
classification math.MGmath.CA
keywords chordminkowskiproblemmeasuresassumptionscalledcasescritical
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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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