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math.MG2026
The Mahler Conjecture in Three Dimensions
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
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…
math.MG2026
The Symmetric Mahler Inequality in Dimension Three via Admissible Shadow Systems
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
The three-dimensional symmetric Mahler inequality states that, for every origin-symmetric convex body \(K=-K\subset \mathbb{R}^3\), \[ \VP(K)= |K|\,|K^\circ|\geq \frac{32}{3}. \] I…
math.MG2023
On the planar Gaussian-Minkowski problem
Shibing Chen, Shengnan Hu, Weiru Liu +1
The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgu…