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

Xiong Ge; Yang Kaiwen

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

Analysis of PDEs 2026-08-03 v1 Differential Geometry

Authors: Xiong Ge , Yang Kaiwen

Abstract

For solutions to the Minkowski problem of the even dual curvature measures $\widetilde{C}_q$ in $\mathbb{R}^n$ , $n\ge 2$ , we prove the non-uniqueness for $q>n$ and $n\ge 2$ , and the uniqueness for $0<q<n$ and $n=2$ . These results are governed by our established logarithmic Brunn-Minkowski inequality for dual quermassintegrals $\widetilde V_q$ .

Keywords

Minkowski problem dual curvature measures dual quermassintegrals logarithmic Brunn-Minkowski inequality uniqueness non-uniqueness

Cite

@article{arxiv.2608.01912,
  title  = {The uniqueness and non-uniqueness of solutions to the even dual Minkowski problem},
  author = {Xiong Ge and Yang Kaiwen},
  journal= {arXiv preprint arXiv:2608.01912},
  year   = {2026}
}

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16 pages