dc.contributor.author
Bobenko, Alexander I.
dc.contributor.author
Bücking, Ulrike
dc.date.accessioned
2021-09-03T13:42:10Z
dc.date.available
2021-09-03T13:42:10Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/31825
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-31558
dc.description.abstract
We 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.format.extent
30 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Discrete analytic function
en
dc.subject
Riemann surface
en
dc.subject
Period matrix
en
dc.subject
Discrete holomorphic integral
en
dc.subject
Dirichlet energy
en
dc.subject
Approximation
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
23
dcterms.bibliographicCitation.doi
10.1007/s11040-021-09394-2
dcterms.bibliographicCitation.journaltitle
Mathematical Physics, Analysis and Geometry
dcterms.bibliographicCitation.number
3
dcterms.bibliographicCitation.volume
24
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s11040-021-09394-2
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik
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refubium.funding
Springer Nature DEAL
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
1572-9656
refubium.resourceType.provider
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