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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 131, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.131 (Mi sigma1668) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary

Annegret Burtschera, Christian Kettererb, Robert J. McCannb, Eric Woolgarc

a Department of Mathematics, IMAPP, Radboud University, PO Box 9010, Postvak 59, 6500 GL Nijmegen, The Netherlands
b Department of Mathematics, University of Toronto, 40 St George St, Toronto Ontario, Canada M5S 2E4
c Department of Mathematical and Statistical Sciences and Theoretical Physics Institute, University of Alberta, Edmonton AB, Canada T6G 2G1
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DOI: https://doi.org/10.3842/SIGMA.2020.131
Abstract: 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.
Keywords: curvature-dimension condition, synthetic mean curvature, optimal transport, comparison geometry, diameter bounds, singularity theorems, inscribed radius, inradius bounds, rigidity, measure contraction property.
Funding agency Grant number
Netherlands Organization for Scientific Research VI.Veni.192.208
Deutsche Forschungsgemeinschaft 396662902
Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN–2015–04383
2020–04162
RGPIN-2017-04896
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 Krümmungsschranken durch Methoden des optimal Transports”. RM's research is supported in part by NSERC Discovery Grants RGPIN–2015–04383 and 2020–04162. EW’s research is supported in part by NSERC Discovery Grant RGPIN-2017-04896.
Received: June 3, 2020; in final form November 21, 2020; Published online December 10, 2020
Bibliographic databases:
Document Type: Article
MSC: 51K10, 53C21, 30L99, 83C75
Language: English
Citation: Annegret Burtscher, Christian Ketterer, Robert J. McCann, Eric Woolgar, “Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary”, SIGMA, 16 (2020), 131, 29 pp.
Citation in format AMSBIB
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