Numerical calculation method for function integration on submanifolds of $\mathbb{R}^n$ or compact Riemannian manifolds
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917781761425408 |
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| author | Deng, Fusheng Huang, Gang Wu, Yingyi |
| author_facet | Deng, Fusheng Huang, Gang Wu, Yingyi |
| contents | In this paper, we present a method for digitally representing the "volume element" and calculating the integral of a function on compact hypersurfaces with or without boundary, and low-dimensional submanifolds in $\mathbb{R}^n$. We also extend such calculation to hypersurfaces in compact Riemannnian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical calculation method for function integration on submanifolds of $\mathbb{R}^n$ or compact Riemannian manifolds Deng, Fusheng Huang, Gang Wu, Yingyi Numerical Analysis Differential Geometry In this paper, we present a method for digitally representing the "volume element" and calculating the integral of a function on compact hypersurfaces with or without boundary, and low-dimensional submanifolds in $\mathbb{R}^n$. We also extend such calculation to hypersurfaces in compact Riemannnian manifolds. |
| title | Numerical calculation method for function integration on submanifolds of $\mathbb{R}^n$ or compact Riemannian manifolds |
| topic | Numerical Analysis Differential Geometry |
| url | https://arxiv.org/abs/2409.14151 |