The Lp chord Minkowski problem in a critical interval

Lujun Guo; Dongmeng Xi; Yiming Zhao

doi:10.1007/s00208-023-02721-8

The L_p chord Minkowski problem in a critical interval

Lujun Guo, Dongmeng Xi, Yiming Zhao

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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≤p<1, without symmetry assumptions.

Original language	English (US)
Pages (from-to)	3123-3162
Number of pages	40
Journal	Mathematische Annalen
Volume	389
Issue number	3
DOIs	https://doi.org/10.1007/s00208-023-02721-8
State	Published - Jul 2024

Keywords

52A38
52A40

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00208-023-02721-8

Cite this

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AU - Xi, Dongmeng

AU - Zhao, Yiming

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.

PY - 2024/7

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N2 - Chord measures and Lp 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 Lp chord measure is known as the Lp chord Minkowski problem, which includes the Lp Minkowski problem heavily studied in the past 2 decades as special cases. In the current work, we solve the Lp chord Minkowski problem when 0≤p<1, without symmetry assumptions.

AB - Chord measures and Lp 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 Lp chord measure is known as the Lp chord Minkowski problem, which includes the Lp Minkowski problem heavily studied in the past 2 decades as special cases. In the current work, we solve the Lp chord Minkowski problem when 0≤p<1, without symmetry assumptions.

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