The non-symmetric Mahler conjecture in dimension three

Shibing Chen; Yuanyuan Li; Dongmeng Xi; Zhefeng Xu

The non-symmetric Mahler conjecture in dimension three

Metric Geometry 2026-05-22 v2

Authors: Shibing Chen , Yuanyuan Li , Dongmeng Xi , Zhefeng Xu

Abstract

We prove the non-symmetric Mahler conjecture in dimension three. More precisely, we prove the sharp lower bound $\mathcal P(K) \geq \frac{64}{9}$ for every convex body $K \subset \mathbb R^3$ , where $\mathcal P(K)$ denotes the non-symmetric volume product with respect to the Santal\'o point.

Keywords

Mahler conjecture non-symmetric convex body volume product Santaló point

Cite

@article{arxiv.2605.09334,
  title  = {The non-symmetric Mahler conjecture in dimension three},
  author = {Shibing Chen and Yuanyuan Li and Dongmeng Xi and Zhefeng Xu},
  journal= {arXiv preprint arXiv:2605.09334},
  year   = {2026}
}

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