Isometric Representation of Lipschitz-Free Spaces over Connected Orientable Riemannian Manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915498565828608 |
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| author | Luggin, Franz |
| author_facet | Luggin, Franz |
| contents | We show that the Lipschitz-Free Space over a connected orientable $n$-di\-men\-sio\-nal Riemannian manifold $M$ is isometrically isomorphic to a quotient of $L^1(M,TM)$, the integrable sections of the tangent bundle $TM$, if $M$ is either complete or lies isometrically inside a complete manifold $N$. Two functions are deemed equivalent in this quotient space if their difference has distributional divergence zero.
This quotient is the pre-annihilator of the exact essentially bounded currents, and if $M$ is simply connected, one may replace ``exact'' with ``closed'' currents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isometric Representation of Lipschitz-Free Spaces over Connected Orientable Riemannian Manifolds Luggin, Franz Functional Analysis 46B04 (Primary) 46B20, 46E15, 53C20, 58A30 (Secondary) We show that the Lipschitz-Free Space over a connected orientable $n$-di\-men\-sio\-nal Riemannian manifold $M$ is isometrically isomorphic to a quotient of $L^1(M,TM)$, the integrable sections of the tangent bundle $TM$, if $M$ is either complete or lies isometrically inside a complete manifold $N$. Two functions are deemed equivalent in this quotient space if their difference has distributional divergence zero. This quotient is the pre-annihilator of the exact essentially bounded currents, and if $M$ is simply connected, one may replace ``exact'' with ``closed'' currents. |
| title | Isometric Representation of Lipschitz-Free Spaces over Connected Orientable Riemannian Manifolds |
| topic | Functional Analysis 46B04 (Primary) 46B20, 46E15, 53C20, 58A30 (Secondary) |
| url | https://arxiv.org/abs/2503.04390 |