4 papers
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…
Asymptotic Expansions of the Fundamental Solution for a Mixed Local-Nonlocal Operator
Congming Li, Ling Wang, Jiongduo Xie
In this paper, we study the fundamental solution of the mixed local-nonlocal operator We derive precise asymptotic expansions of the fundamental solution a…
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…
Solutions of the singular Yamabe problem near singular boundaries
Weiming Shen, Zhehui Wang, Jiongduo Xie
In this paper, we investigate the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive optim…