A min-max gap characterization of minimal foliations on the torus

Hoan Nguyen

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arXiv · 2605.12428

A min-max gap characterization of minimal foliations on the torus

Hoan Nguyen

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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.

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BibTeX RIS

Hoan Nguyen. 2026-05-12. A min-max gap characterization of minimal foliations on the torus. https://arxiv.org/abs/2605.12428

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