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arXiv · 2608.18428

Minimal foliations, codimension-one stable norms, and a question of Bangert

Hoan Nguyen
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Abstract

We compute the codimension-one stable norm for a natural class of cohomogeneity-one metrics on tori. In every dimension $n\ge3$, the formula yields smooth nonflat metrics for which each primitive codimension-one homology class is represented by a foliation of calibrated tori, giving a negative answer to a question of Bangert. On $\mathbb T^3$, we construct an infinite-dimensional family of nonflat metrics whose codimension-one stable norm agrees exactly with that of the unit cubic flat torus and whose total volume is fixed. An explicit two-parameter subfamily contains pairwise non-isometric metrics. These examples also show that the Euclidean-stable-norm-and-volume data are not locally injective near the cubic flat metric.

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Hoan Nguyen. 2026-08-19. Minimal foliations, codimension-one stable norms, and a question of Bangert. https://arxiv.org/abs/2608.18428

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