Year: 2026
Type: preprint
Abstract: We solve the oriented asymptotic Plateau problem for integral currents of arbitrary codimension in conformally compact asymptotically locally hyperbolic manifolds without global curvature assumptions. This extends Anderson's theorem in hyperbolic space. A new ingredient is the construction of a barrier hull near conformal infinity, which serves as a barrier for area minimizing currents and stationary varifolds. In the conformally compact setting, the associated convex hull identity extends Anderson's result beyond globally pinched negative curvature.
Source: arXiv (Cornell University)
Author: Wood, Aidan F.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204869161