Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary
Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm, and Villani. We prove a sharp upper bound on the inscribed radius of any subset whose boundary has a suitably signed l...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211088 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary. Annegret Burtscher, Christian Ketterer, Robert J. McCann and Eric Woolgar. SIGMA 16 (2020), 131, 29 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706400123158528 |
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| author | Burtscher, Annegret Ketterer, Christian McCann, Robert J. Woolgar, Eric |
| author_facet | Burtscher, Annegret Ketterer, Christian McCann, Robert J. Woolgar, Eric |
| citation_txt | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary. Annegret Burtscher, Christian Ketterer, Robert J. McCann and Eric Woolgar. SIGMA 16 (2020), 131, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm, and Villani. We prove a sharp upper bound on the inscribed radius of any subset whose boundary has a suitably signed lower bound on its generalized mean curvature. This provides a nonsmooth analog to a result of Kasue (1983) and Li (2014). We prove a stability statement concerning such bounds and - in the Riemannian curvature-dimension (RCD) setting - characterize the cases of equality.
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| first_indexed | 2026-03-19T00:30:40Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211088 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T00:30:40Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Burtscher, Annegret Ketterer, Christian McCann, Robert J. Woolgar, Eric 2025-12-23T13:12:30Z 2020 Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary. Annegret Burtscher, Christian Ketterer, Robert J. McCann and Eric Woolgar. SIGMA 16 (2020), 131, 29 pages 1815-0659 2020 Mathematics Subject Classification: 51K10; 53C21; 30L99; 83C75 arXiv:2005.07435 https://nasplib.isofts.kiev.ua/handle/123456789/211088 https://doi.org/10.3842/SIGMA.2020.131 Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm, and Villani. We prove a sharp upper bound on the inscribed radius of any subset whose boundary has a suitably signed lower bound on its generalized mean curvature. This provides a nonsmooth analog to a result of Kasue (1983) and Li (2014). We prove a stability statement concerning such bounds and - in the Riemannian curvature-dimension (RCD) setting - characterize the cases of equality. The authors are grateful to Yohei Sakurai for directing us to the work of Kasue and to the anonymous referees for their very constructive comments. AB is supported by the Dutch Research Council (NWO), Project number VI.Veni.192.208. CK is funded by the Deutsche Forschungsgemeinschaft (DFG) Projektnummer 396662902, Synthetische Krummungsschranken durch Methoden des optimalen Transports . RMs research is supported in part by NSERC Discovery Grants RGPIN201504383 and 202004162. EW's research is supported in part by NSERC Discovery Grant RGPIN-2017-04896. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary Article published earlier |
| spellingShingle | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary Burtscher, Annegret Ketterer, Christian McCann, Robert J. Woolgar, Eric |
| title | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary |
| title_full | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary |
| title_fullStr | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary |
| title_full_unstemmed | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary |
| title_short | Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary |
| title_sort | inscribed radius bounds for lower ricci bounded metric measure spaces with mean convex boundary |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211088 |
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