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A Weyl's Law for Singular Riemannian Foliations with Applications to Invariant Theory
- Publication Year :
- 2023
-
Abstract
- We prove a version of Weyl's Law for the basic spectrum of a closed singular Riemannian foliation $(M,\mathcal{F})$ with basic mean curvature. In the special case of $M=\mathbb{S}^n$, this gives an explicit formula for the volume of the leaf space $\mathbb{S}^n/\mathcal{F}$ in terms of the algebra of basic polynomials. In particular, $\operatorname{Vol}(\mathbb{S}^n/\mathcal{F})$ is a rational multiple of $\operatorname{Vol}(\mathbb{S}^m)$, where $m=\dim (\mathbb{S}^n/\mathcal{F})$.<br />Comment: 27 pages, 1 figure
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.06533
- Document Type :
- Working Paper