@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct:description """
              This is a preliminary version of my PhD thesis. In this text we discuss possible ways to give quantitative measurement for two spaces not being quasi-isometric. From this quantitative point of view, we reconsider the definition of quasi-isometries and propose a notion of "quasi-isometric distortion growth" between two metric spaces. We revise our article \\cite{Shchur} where an optimal upper-bound for Morse Lemma is given, together with the symmetric variant which we call Anti-Morse Lemma, and their applications. Next, we focus on lower bounds on quasi-isometric distortion growth for hyperbolic metric spaces. In this class, $\\LL^p$-cohomology spaces provides useful quasi-isometry invariants and Poincaré constants of balls are their quantitative incarnation. We study how Poincaré constants are transported by quasi-isometries. For this, we introduce the notion of a cross-kernel. We calculate Poincaré constants for locally homogeneous metrics of the form $dt^2+\\sum_ie^{2\\mu_it}dx_i^2$, and give a lower bound on quasi-isometric distortion growth among such spaces. This allows us to give examples of different quasi-isometric distortion growths, including a sublinear one (logarithmic) provided by unipotent locally homogeneous spaces.
            """ ;
    dct:identifier "hal-00803043" ;
    dct:issued "2026-05-12T05:51:23.921822"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-12T05:51:23.921827"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Quasi-isometries between hyperbolic metric spaces, quantitative aspects" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00803043v1/resource/ef45e407-04b0-4032-b476-049cd42fe063> ;
    dcat:keyword "hyperbolic-space",
        "infoeu-reposemanticspreprint",
        "mathmath-mgmathematics-mathmetric-geometry-mathmg",
        "morse-lemma",
        "poincare-constant",
        "poincare-inequality",
        "preprints-working-papers-",
        "quasi-geodesic",
        "quasi-isometrie" ;
    dcat:landingPage <https://hal.science/hal-00803043> .

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    dct:issued "2026-05-12T05:51:23.951285"^^xsd:dateTime ;
    dct:modified "2026-05-12T05:51:23.906054"^^xsd:dateTime ;
    dct:title "Quasi-isometries between hyperbolic metric spaces, quantitative aspects" ;
    dcat:accessURL <https://hal.science/hal-00803043> .

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<https://hal.science/hal-00803043> a foaf:Document .