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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2605.03938 |
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Table des matières:
- An isoperimetric constant relating length and stable area, or alternatively for hyperbolic manifolds, length and stable commutator length, serves as a Cheeger constant for the smallest eigenvalue of the Hodge Laplacian acting on coexact 1-forms. Using properties of the magnetic geodesic flow associated to the differential of a coexact eigenform, and its behavior at Mañé's critical energy level, we give new proofs of these Cheeger-like inequalities, with improved constants and volume dependence. We also make a few observations about the relationship between Mañé's critical values and the eigenvalues, when the manifold is hyperbolic.