dc.contributor.author Luce, Robert dc.contributor.author Sète, Olivier dc.date.accessioned 2017-05-04T09:32:33Z dc.date.available 2017-05-04T09:32:33Z dc.date.issued 2017-02-02 dc.identifier.uri http://publications.mfo.de/handle/mfo/1282 dc.identifier.uri https://arxiv.org/abs/1701.03847 dc.description Mathematics Subject Classification (2010): 31A05, 30C55 en_US Keywords: Harmonic mappings; Poincaré index; singular zero; multiplicity; critical set dc.description Research in Pairs 2017 en_US dc.description.abstract We study harmonic mappings of the form $f(z) = h(z) - \overline{z}$, where $h$ is an analytic function. In particular we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of $f$, where the Jacobian of $f$ is non-vanishing, it is known that this index has similar properties as the classical multiplicity of zeros of analytic functions. Little is known about the index of zeros on the critical set, where the Jacobian vanishes; such zeros are called singular zeros. Our main result is a characterization of the index of singular zeros, which enables one to determine the index directly from the power series of $h$. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2017,03 dc.subject Harmonic mappings en_US dc.subject Poincaré index en_US dc.subject Singular zero en_US dc.subject Multiplicity en_US dc.subject Critical set en_US dc.title The Index of Singular Zeros of Harmonic Mappings of Anti-Analytic Degree One en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2017-03 local.scientificprogram Research in Pairs 2017 en_US local.series.id OWP-2017-03 local.subject.msc 31 local.subject.msc 30
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