3 papers
math.DG2026
Mass Bounds for Confined Area-Minimizing Minimal Surfaces
Xumin Jiang, Jiongduo Xie
We establish codimension-independent mass bounds for geometrically confined area-minimizing rectifiable currents. In Euclidean space, we combine the confined-volume doubling theore…
math.DG2026
Asymptotics of high-codimensional area-minimizing currents in hyperbolic space
Xumin Jiang, Jiongduo Xie
We investigate the asymptotic behavior of high-codimensional area-minimizing locally rectifiable currents in hyperbolic space, addressing a problem posed by F.H. Lin and establishi…
math.DG2023
The singular sets of degenerate and nonlocal elliptic equations on Poincaré-Einstein manifolds
Xumin Jiang, Yannick Sire, Ruobing Zhang
The main objects of this paper include some degenerate and nonlocal elliptic operators which naturally arise in the conformal invariant theory of Poincaré-Einstein manifolds. These…