Harmonic shears of slit and polygonal mappings

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Ponnusamy, Saminathan
dc.contributor.author Quach, Tri
dc.contributor.author Rasila, Antti
dc.date.accessioned 2013-02-06T09:30:06Z
dc.date.available 2013-02-06T09:30:06Z
dc.date.issued 2012
dc.identifier.isbn 978-952-60-4520-7 (electronic)
dc.identifier.issn 1799-490X (electronic)
dc.identifier.issn 1799-4896 (ISSN-L)
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/7719
dc.description.abstract In this paper, we study harmonic mappings by using the shear construction, introduced by Clunie and Sheil-Small in 1984. We consider two classes of conformal mappings, each of which maps the unit disk D univalently onto a domain which is convex in the horizontal direction, and shear these mappings with suitable dilatations !. Mappings of the first class map the unit disk D onto four-slit domains and mappings of the second class take D onto regular n-gons. In addition, we discuss the minimal surfaces associated with such harmonic mappings. Furthermore, illustrations of mappings and associated minimal surfaces are given by using MATHEMATICA. en
dc.format.extent 21
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Aalto University en
dc.publisher Aalto-yliopisto fi
dc.relation.ispartofseries Aalto University publication series SCIENCE+TECHNOLOGY en
dc.relation.ispartofseries 3/2012
dc.subject.other Mathematics en
dc.title Harmonic shears of slit and polygonal mappings en
dc.type D4 Julkaistu kehittämis- tai tutkimusraportti tai -selvitys fi
dc.contributor.school Perustieteiden korkeakoulu fi
dc.contributor.school School of Science en
dc.contributor.department Matematiikan ja systeemianalyysin laitos fi
dc.contributor.department Department of Mathematics and Systems Analysis en
dc.subject.keyword harmonic univalent mappings en
dc.subject.keyword convex along wear directions en
dc.subject.keyword convex functions en
dc.subject.keyword harmonic shear en
dc.subject.keyword polygonal mappings en
dc.subject.keyword slit mappings en
dc.subject.keyword minimal surfaces en
dc.subject.keyword AMS:30C99
dc.subject.keyword AMS:30C62
dc.subject.keyword AMS:31A62
dc.subject.keyword AMS:53A10
dc.identifier.urn URN:ISBN:978-952-60-4520-7
dc.type.dcmitype text en


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