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Stability of the volume growth rate under quasi-isometries

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorGranados, Ana
dc.contributor.authorPestana Galván, Domingo de Guzmán
dc.contributor.authorPortilla, Ana
dc.contributor.authorRodríguez García, José Manuel
dc.contributor.authorTourís, Eva
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.contributor.funderAgencia Estatal de Investigación (España)es
dc.date.accessioned2023-09-11T12:21:50Z
dc.date.available2023-09-11T12:21:50Z
dc.date.issued2020-01
dc.description.abstractKanai proved powerful results on the stability under quasi-isometries of numerous global properties (including the volume growth rate) between non-bordered Riemannian manifolds of bounded geometry. Since his work focuses more on the generality of the spaces considered than on the two-dimensional geometry, Kanai's hypotheses are not usually satisfied in the context of Riemann surfaces endowed with the Poincaré metric. In this work we try to fill that gap and prove the stability of the volume growth rate by quasi-isometries, under hypotheses that many bordered or non-bordered Riemann surfaces (and even Riemannian surfaces with pinched negative curvature) satisfy. In order to get our results, it is shown that many bordered Riemannian surfaces with pinched negative curvature are bilipschitz equivalent to bordered surfaces with constant negative curvature.en
dc.description.sponsorshipSupported in part by two grants from Ministerio de Economía y Competititvidad, Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2016-78227-C2-1-P and MTM2017-90584-REDT), Spain.en
dc.format.extent40
dc.identifier.bibliographicCitationGranados, A., Pestana, D., Portilla, A., Rodríguez, J. M., & Tourís, E. (2019). Stability of the volume growth rate under quasi-isometries. Revista Matematica Complutense, 33(1), 231-270.en
dc.identifier.doihttps://doi.org/10.1007/s13163-019-00301-6
dc.identifier.issn1139-1138
dc.identifier.publicationfirstpage231
dc.identifier.publicationissue1
dc.identifier.publicationlastpage270
dc.identifier.publicationtitleRevista Matematica Complutensees
dc.identifier.publicationvolume33
dc.identifier.urihttps://hdl.handle.net/10016/38293
dc.identifier.uxxiAR/0000025503
dc.language.isoengen
dc.publisherSpringer Natureen
dc.relation.projectIDGobierno de España. MTM2016-78227-C2-1-Pes
dc.relation.projectIDGobierno de España. MTM2017-90584-REDTes
dc.rights© Universidad Complutense de Madrid 2019es
dc.rights.accessRightsopen accessen
dc.subject.ecienciaMatemáticases
dc.subject.otherNegative pinched curvatureen
dc.subject.otherPoincaré metricen
dc.subject.otherQuasi-isometryen
dc.subject.otherRiemann surfaceen
dc.subject.otherVolume growth rateen
dc.titleStability of the volume growth rate under quasi-isometriesen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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