3 papers
math.AP2026
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…
math.AP2026
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…
math.AP2026
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…