The Lpchord Minkowski problem

Dongmeng Xi; Deane Yang; Gaoyong Zhang; Yiming Zhao

doi:10.1515/ans-2022-0041

The L_pchord Minkowski problem

Dongmeng Xi, Deane Yang, Gaoyong Zhang, Yiming Zhao

Mathematics

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

Abstract

Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n in addition to Aleksandrov-Fenchel-Jessen's area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p chord measures is called the L p chord Minkowski problem in the L p Brunn-Minkowski theory, which includes the L p Minkowski problem as a special case. This article solves the L p chord Minkowski problem when p > 1 and the symmetric case of 0 < p < 1.

Original language	English (US)
Article number	20220041
Journal	Advanced Nonlinear Studies
Volume	23
Issue number	1
DOIs	https://doi.org/10.1515/ans-2022-0041
State	Published - Jan 1 2023

Keywords

L Minkowski problem
L chord Minkowski problem
L chord measure
L surface area measure
chord integral
chord measure

ASJC Scopus subject areas

Statistical and Nonlinear Physics
General Mathematics

Access to Document

10.1515/ans-2022-0041

Cite this

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title = "The Lpchord Minkowski problem",

abstract = "Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n in addition to Aleksandrov-Fenchel-Jessen's area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p chord measures is called the L p chord Minkowski problem in the L p Brunn-Minkowski theory, which includes the L p Minkowski problem as a special case. This article solves the L p chord Minkowski problem when p > 1 and the symmetric case of 0 < p < 1.",

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AU - Xi, Dongmeng

AU - Yang, Deane

AU - Zhang, Gaoyong

AU - Zhao, Yiming

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N2 - Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n in addition to Aleksandrov-Fenchel-Jessen's area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p chord measures is called the L p chord Minkowski problem in the L p Brunn-Minkowski theory, which includes the L p Minkowski problem as a special case. This article solves the L p chord Minkowski problem when p > 1 and the symmetric case of 0 < p < 1.

AB - Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n in addition to Aleksandrov-Fenchel-Jessen's area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p chord measures is called the L p chord Minkowski problem in the L p Brunn-Minkowski theory, which includes the L p Minkowski problem as a special case. This article solves the L p chord Minkowski problem when p > 1 and the symmetric case of 0 < p < 1.

KW - L Minkowski problem

KW - L chord Minkowski problem

KW - L chord measure

KW - L surface area measure

KW - chord integral

KW - chord measure

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