Number and location of pre-images under harmonic mappings in the plane

dc.contributor.authorSète, Olivier
dc.contributor.authorZur, Jan
dc.date.accessioned2022-08-01T14:21:55Z
dc.date.available2022-08-01T14:21:55Z
dc.date.issued2021-06-21
dc.description.abstractWe derive a formula for the number of pre-images under a non-degenerate harmonic mapping f, using the argument principle. This formula reveals a connection between the pre-images and the caustics. Our results allow to deduce the number of pre-images under f geometrically for every non-caustic point. We approximately locate the pre-images of points near the caustics. Moreover, we apply our results to prove that for every k = n, n + 1, ... , n^2 there exists a harmonic polynomial of degree n with k zeros.en
dc.identifier.eissn2737-114X
dc.identifier.issn2737-0690
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/17287
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-16067
dc.language.isoenen
dc.relation.ispartof10.14279/depositonce-15947
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/en
dc.subject.ddc518 Numerische Analysisde
dc.subject.otherharmonic mappingsen
dc.subject.otherpre-imagesen
dc.subject.othercausticsen
dc.subject.otherargument principleen
dc.subject.othervalenceen
dc.subject.otherzeros of harmonic polynomialsen
dc.titleNumber and location of pre-images under harmonic mappings in the planeen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.5186/aasfm.2021.4614en
dcterms.bibliographicCitation.issue1en
dcterms.bibliographicCitation.journaltitleAnnales Fennici Mathematicien
dcterms.bibliographicCitation.originalpublishernameThe Finnish Mathematical Societyen
dcterms.bibliographicCitation.originalpublisherplaceHelsinkien
dcterms.bibliographicCitation.pageend247en
dcterms.bibliographicCitation.pagestart225en
dcterms.bibliographicCitation.volume46en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Numerische Lineare Algebrade
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Lineare Algebrade
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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