The equality case in Cheeger's and Buser's inequalities on RCD spaces
We prove that the sharp Buser’s inequality obtained in the framework of RCD(1, ∞) spaces by the first two authors [29] is rigid, i.e. equality is obtained if and only if the space splits isomorphically a Gaussian. The result is new even in the smooth setting. We also show that the equality in Cheege...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2021
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| _version_ | 1826307527293272064 |
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| author | De Ponti, N Mondino, A Semola, D |
| author_facet | De Ponti, N Mondino, A Semola, D |
| author_sort | De Ponti, N |
| collection | OXFORD |
| description | We prove that the sharp Buser’s inequality obtained in the framework of RCD(1, ∞) spaces by the first two authors [29] is rigid, i.e. equality is obtained if and only if the space splits isomorphically a Gaussian. The result is new even in the smooth setting. We also show that the equality in Cheeger’s inequality is never attained in the setting of RCD(K, ∞) spaces with finite diameter or positive curvature, and we provide several examples of spaces with Ricci curvature bounded below where these assumptions are not satisfied and the equality is attained. |
| first_indexed | 2024-03-07T07:04:26Z |
| format | Journal article |
| id | oxford-uuid:368194e2-b277-42cd-b490-95b9345098a2 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:04:26Z |
| publishDate | 2021 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:368194e2-b277-42cd-b490-95b9345098a22022-04-25T09:44:31ZThe equality case in Cheeger's and Buser's inequalities on RCD spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:368194e2-b277-42cd-b490-95b9345098a2EnglishSymplectic ElementsElsevier2021De Ponti, NMondino, ASemola, DWe prove that the sharp Buser’s inequality obtained in the framework of RCD(1, ∞) spaces by the first two authors [29] is rigid, i.e. equality is obtained if and only if the space splits isomorphically a Gaussian. The result is new even in the smooth setting. We also show that the equality in Cheeger’s inequality is never attained in the setting of RCD(K, ∞) spaces with finite diameter or positive curvature, and we provide several examples of spaces with Ricci curvature bounded below where these assumptions are not satisfied and the equality is attained. |
| spellingShingle | De Ponti, N Mondino, A Semola, D The equality case in Cheeger's and Buser's inequalities on RCD spaces |
| title | The equality case in Cheeger's and Buser's inequalities on RCD spaces |
| title_full | The equality case in Cheeger's and Buser's inequalities on RCD spaces |
| title_fullStr | The equality case in Cheeger's and Buser's inequalities on RCD spaces |
| title_full_unstemmed | The equality case in Cheeger's and Buser's inequalities on RCD spaces |
| title_short | The equality case in Cheeger's and Buser's inequalities on RCD spaces |
| title_sort | equality case in cheeger s and buser s inequalities on rcd spaces |
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