The splitting theorem in non-smooth context
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| _version_ | 1866911630988673024 |
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| author | Gigli, Nicola |
| author_facet | Gigli, Nicola |
| contents | We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space. By `infinitesimally Hilbertian' we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1302_5555 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | The splitting theorem in non-smooth context Gigli, Nicola Metric Geometry Differential Geometry 53Cxx, 51Fxx We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space. By `infinitesimally Hilbertian' we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence. |
| title | The splitting theorem in non-smooth context |
| topic | Metric Geometry Differential Geometry 53Cxx, 51Fxx |
| url | https://arxiv.org/abs/1302.5555 |