Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs

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Show simple item record Rodríguez García, José Manuel Martínez Pérez, Alvaro 2021-05-13T08:33:22Z 2021-05-13T08:33:22Z 2018-08-01
dc.identifier.bibliographicCitation Martínez-Pérez, A., and Rodríguez, J. M. (2018). Cheeger isoperimetric constant of gromov hyperbolic manifolds and graphs. Communications in Contemporary Mathematics, 20(05), 1750050
dc.identifier.issn 0219-1997
dc.description.abstract In this paper, we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying this isoperimetric inequality, in terms of their Gromov boundary. Furthermore, we characterize the trees with isoperimetric inequality (without any hypothesis). As an application of our results, we obtain the solvability of the Dirichlet problem at infinity for these Riemannian manifolds and graphs, and that the Martin boundary is homeomorphic to the Gromov boundary.
dc.description.sponsorship Supported in part by a grant from Ministerio de Economíıa y Competitividad (MTM 2012-30719), Spain. Supported in part by two grants from Ministerio de Economíıa y Competitividad (MTM 2013-46374-P and MTM 2015- 69323-REDT), Spain, and a grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México.
dc.format.extent 24 p.
dc.language.iso eng
dc.publisher World Scientific Publishing
dc.rights © World Scientific Publishing
dc.subject.other Gromov hyperbolicity
dc.subject.other Cheeger isoperimetric constant
dc.subject.other Bounded local geometry
dc.title Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2016-78227-C2-1-P
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1750050
dc.identifier.publicationissue 5
dc.identifier.publicationtitle Communications in Contemporary Mathematics
dc.identifier.publicationvolume 20
dc.identifier.uxxi AR/0000021691
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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