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Isoperimetric Inequalities in Riemann Surfaces and Graphs

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dc.contributor.authorMartínez Pérez, Álvaro
dc.contributor.authorRodríguez, José M.
dc.date.accessioned2025-12-16T09:21:51Z
dc.date.available2025-12-16T09:21:51Z
dc.date.issued2021
dc.description.abstractA celebrated theorem of Kanai states that quasi-isometries preserve isoperimetric inequalities between uniform Riemannian manifolds (with positive injectivity radius) and graphs. Our main result states that we can study the (Cheeger) isoperimetric inequality in a Riemann surface by using a graph related to it, even if the surface has injectivity radius zero (this graph is inspired in Kanai’s graph, but it is different from it). We also present an application relating Gromov boundary and isoperimetric inequality.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia, Innovacion y Universidades
dc.description.sponsorshipMinisterio de Economa y Competititvidad
dc.description.sponsorshipAgencia Estatal de Investigacion
dc.description.sponsorshipFondo Europeo de Desarrollo Regional (FEDER)
dc.description.statuspub
dc.identifier.citationMartínez-Pérez, Á., Rodríguez, J.M. Isoperimetric Inequalities in Riemann Surfaces and Graphs. J Geom Anal.2021; 31: 3583–3607.
dc.identifier.doi10.1007/s12220-020-00407-0
dc.identifier.issn1050-6926
dc.identifier.issn1559-002X
dc.identifier.urihttps://hdl.handle.net/20.500.14352/129071
dc.journal.titleThe Journal fo Geometric Analysis
dc.language.isoeng
dc.page.final3607
dc.page.initial3583
dc.publisherSpringer Nature Link
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-098321-B-I00/ES/COMBINATORIA Y DINAMICA: ASPECTOS GEOMETRICOS Y TOPOLOGICOS EN VARIEDADES/
dc.relation.projectIDMTM2016-78227-C2-1-P
dc.relation.projectIDMTM2017-90584-REDT
dc.rights.accessRightsopen access
dc.subject.keywordCheeger isoperimetric constant
dc.subject.keywordGromov hyperbolicity
dc.subject.keywordIsoperimetric inequality
dc.subject.keywordPoincaré metric
dc.subject.keywordRiemann surface
dc.subject.ucmGeometría diferencial
dc.subject.unesco1204.04 Geometría Diferencial
dc.titleIsoperimetric Inequalities in Riemann Surfaces and Graphs
dc.typejournal article
dc.volume.number31
dspace.entity.typePublication

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