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

dc.contributorAalto Universityen
dc.contributor.authorRadnell, Daviden_US
dc.contributor.authorSchippers, Ericen_US
dc.contributor.authorStaubach, Wolfgangen_US
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.contributor.organizationUniversity of Manitobaen_US
dc.contributor.organizationUppsala Universityen_US
dc.description.abstractConsider 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.description.versionPeer revieweden
dc.identifier.citationRadnell, 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 .
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dc.relation.ispartofseriesCommunications in Contemporary Mathematicsen
dc.relation.ispartofseriesVolume 19, issue 01en
dc.subject.keyword(Formula presented.) Beltrami differentialsen_US
dc.subject.keywordbordered Riemann surfacesen_US
dc.subject.keywordGardiner–Schiffer variationen_US
dc.subject.keywordinfinitesimally trivial Beltrami differentialsen_US
dc.subject.keywordTeichmüller theoryen_US
dc.subject.keywordWeil–Petersson metricen_US
dc.titleConvergence of the Weil–Petersson metric on the Teichmüller space of bordered Riemann surfacesen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi