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Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities

In: Modern Discrete Mathematics and Analysis

Author

Listed:
  • Chang-Jian Zhao

    (China Jiliang University)

  • Wing Sum Cheung

    (The University of Hong Kong)

Abstract

We further consider the Orlicz dual Brunn-Minkowski theory. An Orlicz radial harmonic addition is introduced, which generalizes the L p-radial addition and the L p-harmonic addition to an Orlicz space, respectively. The variational formula for the dual mixed quermassintegrals with respect to the Orlicz radial harmonic addition is proved, and the new Orlicz dual quermassintegrals generalizes the L p-dual quermassintegrals. The fundamental notions and conclusions of the dual quermassintegrals and the Minkoswki and Brunn-Minkowski inequalities for the dual quermassintegrals are extended to an Orlicz setting. The new Orlicz-Minkowski and Brunn-Minkowski inequalities in special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn-Minkowski inequality, which also imply the L p-dual Minkowski inequality and L p-dual Brunn-Minkowski inequality for the dual quermassintegrals. As application, a dual log-Minkowski inequality is proved.

Suggested Citation

  • Chang-Jian Zhao & Wing Sum Cheung, 2018. "Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Modern Discrete Mathematics and Analysis, pages 11-37, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-74325-7_2
    DOI: 10.1007/978-3-319-74325-7_2
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