The Lpchord Minkowski problem

Dongmeng Xi, Deane Yang, Gaoyong Zhang, Yiming Zhao

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number20220041
JournalAdvanced Nonlinear Studies
Issue number1
StatePublished - Jan 1 2023


  • 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


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