The $L_p$ Chord Minkowski problem in a critical interval
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, wh...
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| Zusammenfassung: | 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 |
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| DOI: | 10.48550/arxiv.2301.07603 |