A Weyl’s law for singular Riemannian foliations with applications to invariant theory

Lin, Samuel; Mendes, Ricardo A E; Radeschi, Marco

doi:10.2140/gt.2025.29.3873

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A Weyl's law for singular Riemannian foliations with applications to invariant theory

Samuel Lin, Ricardo A E Mendes and Marco Radeschi

Geometry & Topology 29 (2025) 3873–3904

DOI: 10.2140/gt.2025.29.3873

Abstract

We prove a version of Weyl’s law for the basic spectrum of a closed singular Riemannian foliation $(M, ℱ)$ with basic mean curvature. In the special case of $M = 𝕊^{n}$ , this gives an explicit formula for the volume of the leaf space $𝕊^{n} ∕ ℱ$ in terms of the algebra of basic polynomials. In particular, $Vol (𝕊^{n} ∕ ℱ)$ is a rational multiple of $Vol (𝕊^{m})$ , where $m = \dim (𝕊^{n} ∕ ℱ)$ .

Keywords

Weyl's law, singular Riemannian foliations

Mathematical Subject Classification

Primary: 53C12

References

Publication

Received: 10 January 2024

Revised: 29 October 2024

Accepted: 20 February 2025

Published: 10 October 2025

Proposed: Urs Lang

Seconded: Roman Sauer, David Fisher

Authors

Samuel Lin
Department of Mathematics University of Oklahoma Norman, OK United States	Colby College Waterville, MA United States

Ricardo A E Mendes
Department of Mathematics University of Oklahoma Norman, OK United States

Marco Radeschi
Dipartimento di matematica “G Peano” Università degli Studi di Torino Torino Italy

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Volume 29, issue 7 (2025)