Convergence speed for the average density of eigenfunctions for singular Riemannian manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918301707272192 |
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| author | Dietze, Charlotte |
| author_facet | Dietze, Charlotte |
| contents | We consider a class of singular Riemannian metrics on a compact Riemannian manifold with boundary and the eigenfunctions of the corresponding Laplace-Beltrami operator. In our setting, the average density of eigenfunctions with eigenvalue less than $λ$ converges weakly to the uniform normalised measure on the boundary as $λ\to\infty$. In this work, we show a quantitative estimate on the speed of this convergence in the Wasserstein-sense in the transverse coordinate to the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence speed for the average density of eigenfunctions for singular Riemannian manifolds Dietze, Charlotte Analysis of PDEs Spectral Theory We consider a class of singular Riemannian metrics on a compact Riemannian manifold with boundary and the eigenfunctions of the corresponding Laplace-Beltrami operator. In our setting, the average density of eigenfunctions with eigenvalue less than $λ$ converges weakly to the uniform normalised measure on the boundary as $λ\to\infty$. In this work, we show a quantitative estimate on the speed of this convergence in the Wasserstein-sense in the transverse coordinate to the boundary. |
| title | Convergence speed for the average density of eigenfunctions for singular Riemannian manifolds |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2601.16574 |