Quasidisks and Twisting of the Riemann Map

István Prause

Type: Article

Publication Date: 2017-07-07

Citations: 2

DOI: https://doi.org/10.1093/imrn/rnx173

Abstract

Consider a conformal map from the unit disk onto a quasidisk. We determine a range of critical complex powers with respect to which the derivative is integrable. The results fit into the picture predicted by a circular analogue of Brennan's conjecture.

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	A quasiconformal analogue of brennan's conjecture	1998	Ritva Hurri-Syrjänen Susan Staples
+	Quasicircles and hyperbolic zero packing	2022	Håakan Hedenmalm
+ PDF Chat	Quasiconformal Homeomorphisms Explicitly Determining the Basic Curve Quasi-Invariants	2023	Samuel L. Krushkal
+	Quasiconformal mapping	2023	Richard Beals Roderick Wong
+ PDF Chat	Holomorphic isometries between products of complex unit balls	2017	Shan Tai Chan Ming Xiao Yuan Yuan
+	Holomorphic isometries between products of complex unit balls	2017	Shan Tai Chan Ming Xiao Yuan Yuan
+ PDF Chat	Level Sets of the Hyperbolic Derivative for Analytic Self-Maps of the Unit Disk	2021	Juan José Arango Hugo Arbeláez Diego Mejía
+ PDF Chat	Decreasing dilatation can increase dimension	2007	Christopher J. Bishop
+	Level sets of the Hyperbolic Derivative for analytic self-maps of the unit disk	2019	Juan José Arango Hugo Arbeláez Diego Mejía
+	Distortion and topology	2014	Riku Klén Gaven Martin
+	Quasicircles as equipotential lines, homotopy classes and geodesics	2014	Gaven Martin
+	Quasicircles as equipotential lines, homotopy classes and geodesics	2014	Gaven Martin
+ PDF Chat	Conformal Mapping in Linear Time	2010	Christopher J. Bishop
+	The Quasi-Additivity Law in Conformal Geometry	2005	Jeremy Kahn Mikhail Lyubich
+ PDF Chat	The quasi-additivity law in conformal geometry	2009	Jeremy Kahn Mikhail Lyubich
+ PDF Chat	Bounded circular distortion curves and quasidisks	2005	Yu‐Ming Chu Zhenjiang Zhao
+	On mappings of finite distortion that are quasiconformal in the unit disk	2021	Olli Hirviniemi Lauri Hitruhin István Prause Eero Saksman
+	Dynamics of quasiregular mappings with constant complex dilatation	2014	Alastair Fletcher R. J. Fryer
+	The conformal mapping on a disk	2014	阮奕彰 Yi-Chang Juan
+ PDF Chat	Quasicircles as equipotential lines, homotopy classes and geodesics	2016	Gaven Martin

Works That Cite This (2)

Action	Title	Year	Authors
+ PDF Chat	On mappings of finite distortion that are quasiconformal in the unit disk	2022	Olli Hirviniemi Lauri Hitruhin István Prause Eero Saksman
+ PDF Chat	Stretching and Rotation of Planar Quasiconformal Mappings on a Line	2021	Olli Hirviniemi István Prause Eero Saksman

Works Cited by This (23)

Action	Title	Year	Authors
+	Pick Interpolation and Hilbert Function Spaces	2002	Jim Agler John E. McCarthy
+	Function theory in polydiscs	1996	Walter Rudin
+ PDF Chat	Asymptotic Variance of the Beurling Transform	2015	Kari Astala Oleg Ivrii Antti Perälä István Prause
+ PDF Chat	Bilipschitz and quasiconformal rotation, stretching and multifractal spectra	2014	Kari Astala Tadeusz Iwaniec István Prause Eero Saksman
+ PDF Chat	Some results connected with Brennan's conjecture	1994	Lennart Carleson Nikolai Makarov
+ PDF Chat	Boundary properties of Green functions in the plane	2008	Anton Baranov Håakan Hedenmalm
+	The Integrability of the Derivative in Conformal Mapping	1978	James E. Brennan
+	Phase transition for the universal bounds on the integral means spectrum	2009	Ilia Binder
+	Boundary Behaviour of Conformal Maps	1992	Christian Pommerenke
+ PDF Chat	Dimension of quasicircles	2010	Stanislav Smirnov