6 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…
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 \[ Δu=χ_{\{|\nabla u|>0\}} \] near the origin. We prove that, at a singular point of \(\partial\{|\nabla u|>0\}\), the quadratic blow-up is uniq…
Global regularity in the Monge-Ampère obstacle problem
Shibing Chen, Jiakun Liu, Xianduo Wang
In this paper, we establish the global estimate for the Monge-Ampère obstacle problem: , where and are positive cont…
Global analyticity of affine hyperbolic spheres in the even dimensional space
Huaiyu Jian, Xianduo Wang
A number of geometric problems, including affine hyperbolic spheres, Hilbert metrics and Minkowski type problems, are reduced to a singular Monge-Ampère equation which can be writt…
Sharp boundary regularity for some degenerate-singular Monge-Ampère Equations on k-convex domain
Huaiyu Jian, Xianduo Wang
We introduce the concept of k-strictly convexity to describe the accurate convexity of convex domains some directions of which boundary may be flat. Basing this accurate convexity,…