Number and location of pre-images under harmonic mappings in the plane
| dc.contributor.author | Sète, Olivier | |
| dc.contributor.author | Zur, Jan | |
| dc.date.accessioned | 2022-08-01T14:21:55Z | |
| dc.date.available | 2022-08-01T14:21:55Z | |
| dc.date.issued | 2021-06-21 | |
| dc.description.abstract | We 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.eissn | 2737-114X | |
| dc.identifier.issn | 2737-0690 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/17287 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-16067 | |
| dc.language.iso | en | en |
| dc.relation.ispartof | 10.14279/depositonce-15947 | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc/4.0/ | en |
| dc.subject.ddc | 518 Numerische Analysis | de |
| dc.subject.other | harmonic mappings | en |
| dc.subject.other | pre-images | en |
| dc.subject.other | caustics | en |
| dc.subject.other | argument principle | en |
| dc.subject.other | valence | en |
| dc.subject.other | zeros of harmonic polynomials | en |
| dc.title | Number and location of pre-images under harmonic mappings in the plane | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.5186/aasfm.2021.4614 | en |
| dcterms.bibliographicCitation.issue | 1 | en |
| dcterms.bibliographicCitation.journaltitle | Annales Fennici Mathematici | en |
| dcterms.bibliographicCitation.originalpublishername | The Finnish Mathematical Society | en |
| dcterms.bibliographicCitation.originalpublisherplace | Helsinki | en |
| dcterms.bibliographicCitation.pageend | 247 | en |
| dcterms.bibliographicCitation.pagestart | 225 | en |
| dcterms.bibliographicCitation.volume | 46 | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Lineare Algebra | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Numerische Lineare Algebra | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |