Dual curvature measures on convex functions and associated Minkowski problems

2021/05/04 by Niufa Fang, Fang, Niufa, Jiazu Zhou +1
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Pharmacological Effects of Medicinal Plants #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2105.01250

openalex publication_date 2021/05/04 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the q-th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the q-th dual curvature measure of convex bodies which defined by Huang, Lutwak, Yang and Zhang. Existence for the functional dual Minkowski problem is showed when q≤0 and the uniqueness part is obtained with some assumptions.

Citations

• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems
• Geometry of log-concave functions: the L_p Asplund sum and the L_p Minkowski problem

Related

• Existence of solutions to the generalized dual Minkowski problem
• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems
• Uniqueness and continuity of the solution to L_p dual Minkowski problem
• The L_p dual Minkowski problem for p>1 and q>0
• The dual Minkowski problem for symmetric convex bodies