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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 \[ Δu=χ_{\{|\nabla u|>0\}} \] near the origin. We prove that, at a singular point of \(\partial\{|\nabla u|>0\}\), the quadratic blow-up is uniq…