Distortion theorems for quasiconformal mappings

In 1994, Astala published his celebrated Area Distortion Theorem for quasiconformal mappings, a groundbreaking result that allowed a number of new results within this area of Analysis to appear during the last two decades. We focus on the consequences that it has on the distortion of Hausdorff measu...

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Detalles Bibliográficos
Autor: Prats, Martí|||0000-0001-8799-6995
Tipo de recurso: tesis de maestría
Fecha de publicación:2011
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:85569
Acceso en línea:https://ddd.uab.cat/record/85569
Access Level:acceso abierto
Palabra clave:Aplicacions quasi-conformes
Hausdorff, Mesures de
Anàlisi matemàtica
Descripción
Sumario:In 1994, Astala published his celebrated Area Distortion Theorem for quasiconformal mappings, a groundbreaking result that allowed a number of new results within this area of Analysis to appear during the last two decades. We focus on the consequences that it has on the distortion of Hausdorff measure. We follow in particular the approach of the article by Lacey, Sawyer and Uriarte-Tuero to the distortion of content, clarifying some point and changing the approach of the bounds for the Beurling transform, where we take the more classical approach of the article by Astala, Clop, Tolsa, Uriarte-Tuero and Verdera instead.