A min-max gap characterization of minimal foliations on the torus
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913119091032064 |
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| author | Nguyen, Hoan |
| author_facet | Nguyen, Hoan |
| contents | 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. As an application, we derive a recurrence property for totally irrational minimal foliations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A min-max gap characterization of minimal foliations on the torus Nguyen, Hoan Differential Geometry Analysis of PDEs Dynamical Systems 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. As an application, we derive a recurrence property for totally irrational minimal foliations. |
| title | A min-max gap characterization of minimal foliations on the torus |
| topic | Differential Geometry Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2605.12428 |