The Lipschitz-volume rigidity problem for metric manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916561358422016 |
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| author | Marti, Denis |
| author_facet | Marti, Denis |
| contents | We prove a Lipschitz-volume rigidity result for $1$-Lipschitz maps of non-zero degree between metric manifolds (metric spaces homeomorphic to a closed oriented manifold) and Riemannian manifolds. The proof is based on degree theory and recent developments of Lipschitz-volume rigidity for integral currents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Lipschitz-volume rigidity problem for metric manifolds Marti, Denis Differential Geometry Metric Geometry 53C23 (Primary) 49Q15, 28A75 (Secondary) We prove a Lipschitz-volume rigidity result for $1$-Lipschitz maps of non-zero degree between metric manifolds (metric spaces homeomorphic to a closed oriented manifold) and Riemannian manifolds. The proof is based on degree theory and recent developments of Lipschitz-volume rigidity for integral currents. |
| title | The Lipschitz-volume rigidity problem for metric manifolds |
| topic | Differential Geometry Metric Geometry 53C23 (Primary) 49Q15, 28A75 (Secondary) |
| url | https://arxiv.org/abs/2501.05974 |