Non-uniqueness of solutions to the dual L_p-Minkowski problem

2019/10/15 by Qi-Rui Li, Jiakun Liu, Li, Qi-Rui +3 · 4 citations
Mathematics · #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Point processes and geometric inequalities #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1910.06879

arxiv created 2019/10/15 · arxiv updated 2019/10/16

Abstract

The dual L_p-Minkowski problem with p<0<q is investigated in this paper. By proving a new existence result of solutions and constructing an example, we obtain the non-uniqueness of solutions to this problem.

Citations

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

Cited by

• The L_p Dual Minkowski Problem for Group-Invariant Convex Bodies
• On p-Brunn-Minkowski and Brascamp-Lieb inequalities
• Compactness of the L_p dual Minkowski problem in ℝ³
• Uniqueness in the near isotropic Lp dual Minkowski problem

Related

• Uniqueness and continuity of the solution to L_p dual Minkowski problem
• Uniqueness in the near isotropic Lp dual Minkowski problem
• On the uniqueness of solutions to the isotropic L_p dual Minkowski problem
• Uniqueness of solutions to the isotropic L_p Gaussian Minkowski problem
• The Logarithmic Minkowski conjecture and the L_p-Minkowski Problem