Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces
The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13]. The proof, which is based on a quantitative differentiation argument, closely f...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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De Gruyter Open
2019
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| _version_ | 1826275730386845696 |
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| author | Antonelli, G Brué, E Semola, D |
| author_facet | Antonelli, G Brué, E Semola, D |
| author_sort | Antonelli, G |
| collection | OXFORD |
| description | The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13]. The proof, which is based on a quantitative differentiation argument, closely follows the original one. As a simple outcome we provide a volume estimate for the enlargement of Gigli-DePhilippis’ boundary ([20, Remark 3.8]) of ncRCD(K, N) spaces.
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| first_indexed | 2024-03-06T23:03:13Z |
| format | Journal article |
| id | oxford-uuid:62e49bc0-d739-4441-ba7d-25dbdbf7cf57 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:03:13Z |
| publishDate | 2019 |
| publisher | De Gruyter Open |
| record_format | dspace |
| spelling | oxford-uuid:62e49bc0-d739-4441-ba7d-25dbdbf7cf572022-03-26T18:09:18ZVolume bounds for the quantitative singular strata of non collapsed RCD metric measure spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:62e49bc0-d739-4441-ba7d-25dbdbf7cf57EnglishSymplectic ElementsDe Gruyter Open2019Antonelli, GBrué, ESemola, DThe aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13]. The proof, which is based on a quantitative differentiation argument, closely follows the original one. As a simple outcome we provide a volume estimate for the enlargement of Gigli-DePhilippis’ boundary ([20, Remark 3.8]) of ncRCD(K, N) spaces. |
| spellingShingle | Antonelli, G Brué, E Semola, D Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces |
| title | Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces |
| title_full | Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces |
| title_fullStr | Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces |
| title_full_unstemmed | Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces |
| title_short | Volume bounds for the quantitative singular strata of non collapsed RCD metric measure spaces |
| title_sort | volume bounds for the quantitative singular strata of non collapsed rcd metric measure spaces |
| work_keys_str_mv | AT antonellig volumeboundsforthequantitativesingularstrataofnoncollapsedrcdmetricmeasurespaces AT bruee volumeboundsforthequantitativesingularstrataofnoncollapsedrcdmetricmeasurespaces AT semolad volumeboundsforthequantitativesingularstrataofnoncollapsedrcdmetricmeasurespaces |