A Weyl's Law for Singular Riemannian Foliations with Applications to Invariant Theory
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866909845099118592 |
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| author | Lin, Samuel Mendes, Ricardo A. E. Radeschi, Marco |
| author_facet | Lin, Samuel Mendes, Ricardo A. E. Radeschi, Marco |
| contents | 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 $m=\dim (\mathbb{S}^n/\mathcal{F})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06533 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Weyl's Law for Singular Riemannian Foliations with Applications to Invariant Theory Lin, Samuel Mendes, Ricardo A. E. Radeschi, Marco Differential Geometry Commutative Algebra Analysis of PDEs Spectral Theory 53C12 (Primary) 53C20, 53C21, 57S15, 58J50, 35P20, 13A50 (Secondary) 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 $m=\dim (\mathbb{S}^n/\mathcal{F})$. |
| title | A Weyl's Law for Singular Riemannian Foliations with Applications to Invariant Theory |
| topic | Differential Geometry Commutative Algebra Analysis of PDEs Spectral Theory 53C12 (Primary) 53C20, 53C21, 57S15, 58J50, 35P20, 13A50 (Secondary) |
| url | https://arxiv.org/abs/2312.06533 |