The canonical lamination calibrated by a cohomology class

Backus, Aidan

doi:10.2140/gt.2026.30.1575

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ISSN (electronic): 1364-0380

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The canonical lamination calibrated by a cohomology class

Aidan Backus

Geometry & Topology 30 (2026) 1575–1608

DOI: 10.2140/gt.2026.30.1575

Abstract

Let $ρ$ be a unit cohomology class of degree $d - 1$ , on a closed oriented Riemannian manifold of dimension $2 \leq d \leq 7$ . We construct a lamination $λ_{ρ}$ whose leaves are exactly the minimal hypersurfaces calibrated by every calibration in $ρ$ . The geometry of $λ_{ρ}$ is closely related to the geometry of the unit ball of $H_{d - 1} (M, ℝ)$ when it is equipped with Gromov’s stable norm, so our main theorem constrains the shape of the stable unit ball in terms of the topology of $M$ . These results establish a close analogy between the stable norm and Thurston’s earthquake norm on the tangent space to Teichmüller space.

Keywords

laminations, minimal hypersurfaces, calibrations, functions of least gradient, stable norm, Thurston asymmetric metric

Mathematical Subject Classification

Primary: 49Q05

Secondary: 53C38, 37F34

References

Publication

Received: 26 April 2025

Revised: 26 November 2025

Accepted: 15 January 2026

Published: 9 July 2026

Proposed: Tobias H Colding

Seconded: Urs Lang, Leonid Polterovich

Authors

Aidan Backus
Department of Mathematics University of Toronto Toronto, ON Canada

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Volume 30, issue 4 (2026)