Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

dc.contributor.authorBobenko, Alexander I.
dc.contributor.authorBücking, Ulrike
dc.date.accessioned2023-04-06T12:03:09Z
dc.date.available2023-04-06T12:03:09Z
dc.date.issued2021-07-02
dc.date.updated2023-03-25T06:43:26Z
dc.description.abstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere C^. Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.en
dc.description.sponsorshipDFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamik
dc.identifier.eissn1572-9656
dc.identifier.issn1385-0172
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/18506
dc.identifier.urihttps://doi.org/10.14279/depositonce-17315
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.subject.otherdiscrete analytic functionen
dc.subject.otherRiemann surfaceen
dc.subject.otherperiod matrixen
dc.subject.otherdiscrete holomorphic integralen
dc.subject.otherDirichlet energyen
dc.subject.otherapproximationen
dc.titleConvergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphereen
dc.typeArticle
dc.type.versionpublishedVersion
dcterms.bibliographicCitation.articlenumber23
dcterms.bibliographicCitation.doi10.1007/s11040-021-09394-2
dcterms.bibliographicCitation.issue3
dcterms.bibliographicCitation.journaltitleMathematical Physics, Analysis and Geometry
dcterms.bibliographicCitation.originalpublishernameSpringer Nature
dcterms.bibliographicCitation.originalpublisherplaceHeidelberg
dcterms.bibliographicCitation.volume24
dcterms.rightsHolder.referenceCreative-Commons-Lizenz
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::N/A (Not Applicable)
tub.publisher.universityorinstitutionTechnische Universität Berlin

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