The infinitesimal structure of manifolds with non-continuous Riemannian metrics
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912987055390720 |
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| author | Ryborz, Vanessa |
| author_facet | Ryborz, Vanessa |
| contents | This paper investigates the failure of certain metric measure spaces to be infinitesimally Hilbertian or quasi-Riemannian manifolds, by constructing examples arising from a manifold $M$ endowed with a Riemannian metric $g$ that is possibly discontinuous, with $g, g^{-1} \in L^\infty_{\mathrm{loc}} $ and $ g \in W^{1,p}_{\mathrm{loc}}$ for $ p \leq \mathrm{dim} M - 1 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The infinitesimal structure of manifolds with non-continuous Riemannian metrics Ryborz, Vanessa Differential Geometry Metric Geometry This paper investigates the failure of certain metric measure spaces to be infinitesimally Hilbertian or quasi-Riemannian manifolds, by constructing examples arising from a manifold $M$ endowed with a Riemannian metric $g$ that is possibly discontinuous, with $g, g^{-1} \in L^\infty_{\mathrm{loc}} $ and $ g \in W^{1,p}_{\mathrm{loc}}$ for $ p \leq \mathrm{dim} M - 1 $. |
| title | The infinitesimal structure of manifolds with non-continuous Riemannian metrics |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2507.14726 |