Year: 2026
Type: preprint
Abstract: We extend an energy introduced by Mather to the setting of Almgren-Pitts min-max theory and obtain a parametric, higher-dimensional analogue of Mather's variational barrier theory for twist maps and geodesics on tori. We use this energy to establish several criteria for the existence of foliations of the $n$-torus by minimal hypersurfaces. We show that for a generic metric, whenever a lamination by area-minimizing hypersurfaces of the $n$-torus contains a gap, there exists a minimal hypersurface inside the gap that is not area-minimizing. This hypersurface is a higher-dimensional analogue of the secondary minimax orbit appearing in Aubry-Mather theory.
Source: arXiv (Cornell University)
Author: Nguyen, Hoan
Institution: University of Chicago
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161043079