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arXiv · 2608.01912

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

Xiong Ge·Yang Kaiwen
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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 $\widetilde V_q$.

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Xiong Ge, Yang Kaiwen. 2026-08-03. The uniqueness and non-uniqueness of solutions to the even dual Minkowski problem. https://arxiv.org/abs/2608.01912

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