The dual Minkowski problem for negative indices

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52 Scopus citations

Abstract

Recently, the duals of Federer’s curvature measures, called dual curvature measures, were discovered by Huang et al. (Acta Math 216:325–388, 2016). In the same paper, they posed the dual Minkowski problem, the characterization problem for dual curvature measures, and proved existence results when the index, q, is in (0, n). The dual Minkowski problem includes the Aleksandrov problem (q= 0 ) and the logarithmic Minkowski problem (q= n) as special cases. In the current work, a complete solution to the dual Minkowski problem whenever q< 0 , including both existence and uniqueness, is presented.

Original languageEnglish (US)
Article number18
JournalCalculus of Variations and Partial Differential Equations
Volume56
Issue number2
DOIs
StatePublished - Apr 1 2017
Externally publishedYes

Keywords

  • 52A40

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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