Approximating sub-riemannian structures by Riemannian metrics and spectral convergence
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914187759845376 |
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| author | Harakeh, Leo Hillairet, Luc |
| author_facet | Harakeh, Leo Hillairet, Luc |
| contents | We construct an approximating sequence of Riemannian metrics tailored to a given sub-Riemannian structure. We prove that the sequence of associated Riemannian volumes converge to Popp's volume and we then proceed to study the spectral convergence of the associated Laplace operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximating sub-riemannian structures by Riemannian metrics and spectral convergence Harakeh, Leo Hillairet, Luc Differential Geometry Analysis of PDEs Spectral Theory 53C17, 58J50 We construct an approximating sequence of Riemannian metrics tailored to a given sub-Riemannian structure. We prove that the sequence of associated Riemannian volumes converge to Popp's volume and we then proceed to study the spectral convergence of the associated Laplace operators. |
| title | Approximating sub-riemannian structures by Riemannian metrics and spectral convergence |
| topic | Differential Geometry Analysis of PDEs Spectral Theory 53C17, 58J50 |
| url | https://arxiv.org/abs/2512.07621 |