The discrete logarithmic Minkowski problem

• DOI: 10.48550/arxiv.1409.7907
• Publication Date: 2014-01-01
• Authors: Károly J. Böröczky; Pál Hegedűs; Guangxian Zhu
• Keywords: Unit sphere; Minkowski's theorem; Cone (formal languages); Minkowski addition

Existence of solution the logarithmic Minkowski problem is proved for case where discrete measures on unit sphere satisfy subspace concentration condition with respect to some special proper subspaces. In order understand how optimal this is, we discuss certain conditions that any cone volume measure satisfies.