The dual Orlicz-Minkowski problem

2017/03/20 by Baocheng Zhu, Zhu, Baocheng, Sudan Xing +3 · 2 citations
Mathematics · #52A39 #52B45 #53A15 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Morphological variations and asymmetry #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1703.06976

openalex publication_date 2017/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

Cited by

• The Gaussian Minkowski problem for epigraphs of convex functions
• On the general dual Orlicz-Minkowski problem

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