6 papers · 1 filter
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\…
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…
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…
Uniqueness of Blow-ups for the Superconductivity Free Boundary Problem
Shibing Chen, Yuanyuan Li, Xianduo Wang
We study the free-boundary equation \[ Îu=Ï_{\{|\nabla u|>0\}} \] near the origin. We prove that, at a singular point of \(\partial\{|\nabla u|>0\}\), the quadratic blow-up is un…
The chord Minkowski problem for super-critical exponent
Shibing Chen, Qi-Rui Li, Yuanyuan Li
The chord Minkowski problem was recently introduced by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel m…