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Convergence of the Weil–Petersson metric on the Teichmüller space of bordered Riemann surfaces

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Radnell, David
dc.contributor.author Schippers, Eric
dc.contributor.author Staubach, Wolfgang
dc.date.accessioned 2021-05-05T06:19:34Z
dc.date.available 2021-05-05T06:19:34Z
dc.date.issued 2016-06-14
dc.identifier.citation Radnell , D , Schippers , E & Staubach , W 2016 , ' Convergence of the Weil–Petersson metric on the Teichmüller space of bordered Riemann surfaces ' , Communications in Contemporary Mathematics , vol. 19 , no. 01 , 1650025 . https://doi.org/10.1142/S0219199716500255 en
dc.identifier.issn 0219-1997
dc.identifier.other PURE UUID: ba28f849-6f2a-48a5-959d-3127622ca14f
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/ba28f849-6f2a-48a5-959d-3127622ca14f
dc.identifier.other PURE LINK: http://www.scopus.com/inward/record.url?scp=84974779249&partnerID=8YFLogxK
dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/62472534/Weil_Petersson_bordered_surfaces_Radnell_Schippers_Staubach_01_2016.pdf
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/107248
dc.description.abstract Consider a Riemann surface of genus (Formula presented.) bordered by (Formula presented.) curves homeomorphic to the unit circle, and assume that (Formula presented.). For such bordered Riemann surfaces, the authors have previously defined a Teichmüller space which is a Hilbert manifold and which is holomorphically included in the standard Teichmüller space. We show that any tangent vector can be represented as the derivative of a holomorphic curve whose representative Beltrami differentials are simultaneously in (Formula presented.) and (Formula presented.), and furthermore that the space of (Formula presented.) differentials in (Formula presented.) decomposes as a direct sum of infinitesimally trivial differentials and (Formula presented.) harmonic (Formula presented.) differentials. Thus the tangent space of this Teichmüller space is given by (Formula presented.) harmonic Beltrami differentials. We conclude that this Teichmüller space has a finite Weil–Petersson Hermitian metric. Finally, we show that the aforementioned Teichmüller space is locally modeled on a space of (Formula presented.) harmonic Beltrami differentials. en
dc.format.extent 39
dc.format.mimetype application/pdf
dc.language.iso en en
dc.relation.ispartofseries Communications in Contemporary Mathematics en
dc.relation.ispartofseries Volume 19, issue 01 en
dc.rights openAccess en
dc.title Convergence of the Weil–Petersson metric on the Teichmüller space of bordered Riemann surfaces en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.contributor.department Department of Mathematics and Systems Analysis
dc.contributor.department University of Manitoba
dc.contributor.department Uppsala University
dc.subject.keyword (Formula presented.) Beltrami differentials
dc.subject.keyword bordered Riemann surfaces
dc.subject.keyword Gardiner–Schiffer variation
dc.subject.keyword infinitesimally trivial Beltrami differentials
dc.subject.keyword Teichmüller theory
dc.subject.keyword Weil–Petersson metric
dc.identifier.urn URN:NBN:fi:aalto-202105056512
dc.identifier.doi 10.1142/S0219199716500255
dc.type.version acceptedVersion

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