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.
From: Hoan Nguyen [view email]
[v1]
Tue, 12 May 2026 17:24:22 UTC (239 KB)
[v2]
Mon, 22 Jun 2026 20:30:22 UTC (241 KB)
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