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The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3829–3855 | Cite as

The Dual Orlicz–Minkowski Problem

  • Baocheng Zhu
  • Sudan Xing
  • Deping YeEmail author
Article

Abstract

In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the dual Orlicz–Minkowski problem regarding the dual Orlicz curvature measure is provided.

Keywords

Curvature measure Dual curvature measure Dual Minkowski problem Dual Orlicz–Brunn–Minkowski theory \(L_p\) Minkowski problem Orlicz–Brunn–Minkowski theory Orlicz Minkowski problem 

Mathematics Subject Classification

53A15 52B45 52A39 

Notes

Acknowledgements

The first author is supported by AARMS, NSERC, NSFC (No. 11501185), and the Doctor Starting Foundation of Hubei University for Nationalities (No. MY2014B001). The third author is supported by a NSERC grant. We are greatly indebted to the reviewers for many valuable comments which improve largely the quality of the paper.

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of MathematicsHubei University for NationalitiesEnshiChina
  2. 2.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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