Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows
We prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K, N) metric measure spaces; regularity is understood with respect to a newly defined quasi‐metric built from the Green function of the Laplacian. Its main application is that RCD(K, N) spaces have constant dimension...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2019
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| _version_ | 1826272371043991552 |
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| author | Brué, E Semola, D |
| author_facet | Brué, E Semola, D |
| author_sort | Brué, E |
| collection | OXFORD |
| description | We prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K, N) metric measure spaces; regularity is understood with respect to a newly defined quasi‐metric built from the Green function of the Laplacian. Its main application is that RCD(K, N) spaces have constant dimension. In this way we generalize to such an abstract framework a result proved by Colding‐Naber for Ricci limit spaces, introducing ingredients that are new even in the smooth setting. |
| first_indexed | 2024-03-06T22:11:30Z |
| format | Journal article |
| id | oxford-uuid:51f5ff2a-b2d5-4f0f-971a-384e6e76d9fa |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:11:30Z |
| publishDate | 2019 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:51f5ff2a-b2d5-4f0f-971a-384e6e76d9fa2022-03-26T16:22:49ZConstancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flowsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:51f5ff2a-b2d5-4f0f-971a-384e6e76d9faEnglishSymplectic ElementsWiley2019Brué, ESemola, DWe prove a regularity result for Lagrangian flows of Sobolev vector fields over RCD(K, N) metric measure spaces; regularity is understood with respect to a newly defined quasi‐metric built from the Green function of the Laplacian. Its main application is that RCD(K, N) spaces have constant dimension. In this way we generalize to such an abstract framework a result proved by Colding‐Naber for Ricci limit spaces, introducing ingredients that are new even in the smooth setting. |
| spellingShingle | Brué, E Semola, D Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows |
| title | Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows |
| title_full | Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows |
| title_fullStr | Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows |
| title_full_unstemmed | Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows |
| title_short | Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows |
| title_sort | constancy of the dimension for rcd k n spaces via regularity of lagrangian flows |
| work_keys_str_mv | AT bruee constancyofthedimensionforrcdknspacesviaregularityoflagrangianflows AT semolad constancyofthedimensionforrcdknspacesviaregularityoflagrangianflows |