The logarithmic Minkowski problem

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

Research output: Contribution to journalArticle

Abstract

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
Volume26
Issue number3
DOIs
StatePublished - 2013

Fingerprint

Banach spaces
Cones
Logarithmic
Unit Sphere
Unit ball
Analogy
Cone
Banach space
Necessary Conditions
Sufficient Conditions

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The logarithmic Minkowski problem. / Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: Journal of the American Mathematical Society, Vol. 26, No. 3, 2013, p. 831-852.

Research output: Contribution to journalArticle

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