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dc.contributor.authorLuce, Robert
dc.contributor.authorSète, Olivier
dc.date.accessioned2017-05-04T09:32:33Z
dc.date.available2017-05-04T09:32:33Z
dc.date.issued2017-02-02
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1282
dc.identifier.urihttps://arxiv.org/abs/1701.03847
dc.descriptionMathematics Subject Classification (2010): 31A05, 30C55 Keywords: Harmonic mappings; Poincaré index; singular zero; multiplicity; critical seten_US
dc.descriptionResearch in Pairs 2017en_US
dc.description.abstractWe 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.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2017,03
dc.subjectHarmonic mappingsen_US
dc.subjectPoincaré indexen_US
dc.subjectSingular zeroen_US
dc.subjectMultiplicityen_US
dc.subjectCritical seten_US
dc.titleThe Index of Singular Zeros of Harmonic Mappings of Anti-Analytic Degree Oneen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2017-03
local.scientificprogramResearch in Pairs 2017en_US
local.series.idOWP-2017-03
local.subject.msc31
local.subject.msc30


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