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arXiv · 2202.11805

Parametric inequalities and Weyl law for the volume spectrum

Larry Guth·Yevgeny Liokumovich
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Abstract

We show that the Weyl law for the volume spectrum in a compact Riemannian manifold conjectured by Gromov can be derived from parametric generalizations of two famous inequalities: isoperimetric inequality and coarea inequality. We prove two such generalizations in low dimensions and obtain the Weyl law for 1-cycles in 3-manifolds. We also give a new proof of the Almgren isomorphism theorem.

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Larry Guth, Yevgeny Liokumovich. 2022-02-23. Parametric inequalities and Weyl law for the volume spectrum. https://doi.org/10.2140/gt.2025.29.863

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