Noncommutative Laplacian and numerical approximation of Laplace-Beltrami spectrum of compact Riemann surfaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908678540492800 |
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| author | Tageddine, Damien Nave, Jean-Christophe |
| author_facet | Tageddine, Damien Nave, Jean-Christophe |
| contents | We derive a numerical approximation of the Laplace-Beltrami operator on compact surfaces embedded in $\mathbb{R}^3$ with an axial symmetry. To do so we use a noncommutative Laplace operator defined on the space of finite dimensional hermitian matrices. This operator is derived from a foliation of the surface obtained under an $S^1$-action on the surface. We present numerical results in the case of the sphere and a generic ellipsoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noncommutative Laplacian and numerical approximation of Laplace-Beltrami spectrum of compact Riemann surfaces Tageddine, Damien Nave, Jean-Christophe Numerical Analysis We derive a numerical approximation of the Laplace-Beltrami operator on compact surfaces embedded in $\mathbb{R}^3$ with an axial symmetry. To do so we use a noncommutative Laplace operator defined on the space of finite dimensional hermitian matrices. This operator is derived from a foliation of the surface obtained under an $S^1$-action on the surface. We present numerical results in the case of the sphere and a generic ellipsoid. |
| title | Noncommutative Laplacian and numerical approximation of Laplace-Beltrami spectrum of compact Riemann surfaces |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.09909 |