The uniqueness and non-uniqueness of solutions to the even dual Minkowski problem

2026/08/03 by Xiong Ge, Yang Kaiwen
Mathematics · #math.AP #math.DG #msc:52A38 #msc:35J96

paper · pdf

16 pages

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

For solutions to the Minkowski problem of the even dual curvature measures \widetildeC_q in ℝⁿ, n≥ 2, we prove the non-uniqueness for q>n and n≥ 2, and the uniqueness for 0<q<n and n=2. These results are governed by our established logarithmic Brunn-Minkowski inequality for dual quermassintegrals \widetilde V_q.

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