8 papers
Global Regularity in Optimal Transport
Shibing Chen, Yuanyuan Li, Xianduo Wang
In this paper we establish global estimates for the convex potentials of quadratic optimal transport between bounded convex domains with continuous positive densities. Al…
The many-body Blaschke-Santaló type inequality via optimal transport
Shibing Chen, Yuanyuan Li, Dongmeng Xi +1
Let be origin-symmetric measurable sets of finite volume such that \[ \sum_{1\le i<j\le k}\langle x_i,x_j\rangle\le \binom{k}{2}, \qquad \forall\…
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…
Optimal (partial) transport to non-convex polygonal domains
Shibing Chen, Yuanyuan Li, Jiakun Liu
In this paper, we investigate optimal (partial) transport problems for which the target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete optimal transport pro…
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…
On the monotonicity of affine quermassintegrals
Shibing Chen, Yuanyuan Li, Xianduo Wang
Lutwak's affine quermassintegral theory is a foundational component of modern affine Brunn--Minkowski theory. Developed in the 1980s, it provides affine analogues of the classical…