The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3829–3855

# The Dual Orlicz–Minkowski Problem

• Baocheng Zhu
• Sudan Xing
• Deping Ye
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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## Authors and Affiliations

• Baocheng Zhu
• 1
• 2
• Sudan Xing
• 2
• Deping Ye
• 2
1. 1.Department of MathematicsHubei University for NationalitiesEnshiChina
2. 2.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada