Rigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spaces
This note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over RCD(𝐾,𝑁) metric measure spaces. Our main result asserts existence of a Euclidean tangent half-space almost everywhere with respect to the perimeter measure and it can be improved to an existence and uniq...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2019
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| _version_ | 1826293832770125824 |
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| author | Ambrosio, L Brué, E Semola, D |
| author_facet | Ambrosio, L Brué, E Semola, D |
| author_sort | Ambrosio, L |
| collection | OXFORD |
| description | This note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over RCD(𝐾,𝑁) metric measure spaces. Our main result asserts existence of a Euclidean tangent half-space almost everywhere with respect to the perimeter measure and it can be improved to an existence and uniqueness statement when the ambient is non collapsed. As an intermediate tool, we provide a complete characterization of the class of RCD(0,𝑁) spaces for which there exists a nontrivial function satisfying the equality in the 1-Bakry–Émery inequality. This result is of independent interest and it is new, up to our knowledge, even in the smooth framework. |
| first_indexed | 2024-03-07T03:36:15Z |
| format | Journal article |
| id | oxford-uuid:bc618e93-6fac-4971-aa0b-eb628f64c7e1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:36:15Z |
| publishDate | 2019 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:bc618e93-6fac-4971-aa0b-eb628f64c7e12022-03-27T05:24:02ZRigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bc618e93-6fac-4971-aa0b-eb628f64c7e1EnglishSymplectic ElementsSpringer2019Ambrosio, LBrué, ESemola, DThis note is dedicated to the study of the asymptotic behaviour of sets of finite perimeter over RCD(𝐾,𝑁) metric measure spaces. Our main result asserts existence of a Euclidean tangent half-space almost everywhere with respect to the perimeter measure and it can be improved to an existence and uniqueness statement when the ambient is non collapsed. As an intermediate tool, we provide a complete characterization of the class of RCD(0,𝑁) spaces for which there exists a nontrivial function satisfying the equality in the 1-Bakry–Émery inequality. This result is of independent interest and it is new, up to our knowledge, even in the smooth framework. |
| spellingShingle | Ambrosio, L Brué, E Semola, D Rigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spaces |
| title | Rigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spaces |
| title_full | Rigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spaces |
| title_fullStr | Rigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spaces |
| title_full_unstemmed | Rigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spaces |
| title_short | Rigidity of the 1-Bakry–Émery inequality and sets of finite perimeter in RCD spaces |
| title_sort | rigidity of the 1 bakry emery inequality and sets of finite perimeter in rcd spaces |
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