The Mahler Conjecture in Three Dimensions

Shibing Chen; Yuanyuan Li; Dongmeng Xi; Zhe-Feng Xu

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arXiv · 2605.09334

The Mahler Conjecture in Three Dimensions

Shibing Chen·Yuanyuan Li·Dongmeng Xi·Zhe-Feng Xu

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Abstract

The Mahler conjecture dates back to 1938. This paper solves the conjecture for general convex bodies in three dimensions by developing a method called the shadow flow. The equality case is characterized as well. This method is also applied to give a new proof of the three-dimensional symmetric case, which was first proved by Iriyeh--Shibata.

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BibTeX RIS

Shibing Chen, Yuanyuan Li, Dongmeng Xi, Zhe-Feng Xu. 2026-06-15. The Mahler Conjecture in Three Dimensions. https://arxiv.org/abs/2605.09334

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