The logarithmic Minkowski problem

Károly J. Böröczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalArticlepeer-review


In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.

Original languageEnglish (US)
Pages (from-to)831-852
Number of pages22
JournalJournal of the American Mathematical Society
Issue number3
StatePublished - 2013


  • Cone-volume measure
  • Log-Minkowski problem
  • Lp-Minkowski problem
  • Minkowski problem

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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