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dc.contributor.authorAntti, Perälä
dc.date.accessioned2017-03-17T13:41:21Z
dc.date.available2017-03-17T13:41:21Z
dc.date.created2017-03-17
dc.date.issued2017-03-17
dc.identifier.urihttp://hdl.handle.net/10630/13323
dc.description.abstractsymptotic variance can be used to measure the boundary behaviour of conformal maps and Bloch functions. A formula due to McMullen connects it to the Hausdorff dimension expansion of limit sets for certain dynamical families of conformal maps. We introduce the asymptotic variance of the Beurling transform as a tool for studying Hausdorff dimension of quasicircles at infinitesimal level. As a result, we find k-quasicircles with dimension bigger than 1+0.879k^2 for small k. An upper bound for this asymptotic variance can be deduced from Smirnov's quasicircle estimates. Finally, we also mention some very recent (and interesting) advances related to this topic. The talk is based on a joint paper with K. Astala, O. Ivrii and I. Prause.es_ES
dc.language.isoenges_ES
dc.rightsinfo:eu-repo/semantics/openAccesses_ES
dc.subject.otherBeurling transformes_ES
dc.titleAsymptotic variance of the Beurling transformes_ES
dc.typeinfo:eu-repo/semantics/conferenceObjectes_ES
dc.centroFacultad de Cienciases_ES
dc.relation.eventtitleConferenciaes_ES
dc.relation.eventplaceSeminario Departamento Análisis Matemáticoes_ES
dc.relation.eventdate10-05-2017es_ES
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