Journal article
The equality case in Cheeger's and Buser's inequalities on RCD spaces
- Abstract:
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, 507.8KB, Terms of use)
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- Publisher copy:
- 10.1016/j.jfa.2021.109022
Authors
- Publisher:
- Elsevier
- Journal:
- Journal of Functional Analysis More from this journal
- Volume:
- 281
- Issue:
- 3
- Article number:
- 109022
- Publication date:
- 2021-04-07
- Acceptance date:
- 2021-03-18
- DOI:
- ISSN:
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0022-1236
- Language:
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English
- Keywords:
- Pubs id:
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1129774
- Local pid:
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pubs:1129774
- Deposit date:
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2021-04-03
Terms of use
- Copyright holder:
- Elsevier Inc.
- Copyright date:
- 2021
- Rights statement:
- © 2021 Elsevier Inc. All rights reserved.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Elsevier at: https://doi.org/10.1016/j.jfa.2021.109022
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