Approximation of length metrics by conformally flat Riemannian metrics
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916461748944896 |
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| author | Hip, Andres A. Contreras Gwynne, Ewain |
| author_facet | Hip, Andres A. Contreras Gwynne, Ewain |
| contents | We present a proof of the folklore result that any length metric on $\mathbb R^d$ can be approximated by conformally flat Riemannian distance functions in the uniform distance. This result is used to study Liouville quantum gravity in another paper by the same authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of length metrics by conformally flat Riemannian metrics Hip, Andres A. Contreras Gwynne, Ewain Differential Geometry Metric Geometry Probability We present a proof of the folklore result that any length metric on $\mathbb R^d$ can be approximated by conformally flat Riemannian distance functions in the uniform distance. This result is used to study Liouville quantum gravity in another paper by the same authors. |
| title | Approximation of length metrics by conformally flat Riemannian metrics |
| topic | Differential Geometry Metric Geometry Probability |
| url | https://arxiv.org/abs/2410.23304 |