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Quantitative isoperimetry à la Levy-Gromov
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Cavalletti, F., Maggi, F. and Mondino, Andrea (2019) Quantitative isoperimetry à la Levy-Gromov. Communications in Pure and Applied Mathematics, 72 (8). pp. 1631-1677. doi:10.1002/cpa.21808 ISSN 1097-0312.
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WRAP-quantitative-isoperimetry-a-la-Levy-Gromov-Mondino-2018.pdf - Accepted Version - Requires a PDF viewer. Download (782Kb) | Preview |
Official URL: https://doi.org/10.1002/cpa.21808
Abstract
On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of a round sphere of suitable radius. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise. These results are actually obtained in the more general context of (possibly non-smooth) metric measure spaces with curvature-dimension conditions through a quantitative analysis of the transport-rays decompositions obtained by the localization method.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Riemannian manifolds | ||||||||||||
Journal or Publication Title: | Communications in Pure and Applied Mathematics | ||||||||||||
Publisher: | Wiley-Blackwell Publishing, Inc | ||||||||||||
ISSN: | 1097-0312 | ||||||||||||
Official Date: | August 2019 | ||||||||||||
Dates: |
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Volume: | 72 | ||||||||||||
Number: | 8 | ||||||||||||
Page Range: | pp. 1631-1677 | ||||||||||||
DOI: | 10.1002/cpa.21808 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article: Cavalletti, F. , Maggi, F. and Mondino, A. (2019), Quantitative Isoperimetry à la Levy‐Gromov. Comm. Pure Appl. Math. which has been published in final form at https://doi.org/10.1002/cpa.21808. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 20 July 2018 | ||||||||||||
Date of first compliant Open Access: | 1 January 2020 | ||||||||||||
RIOXX Funder/Project Grant: |
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