21 citations · 103 across the 19 of their papers we have counts for
13 papers · 1 filter
Sharp Higher Integrability Theory, Part I: The -norm of the Beurling--Ahlfors transform
Andrea Agazzi, Kari Astala, Giuseppe Bruno +18
We confirm a conjecture posed by T. Iwaniec in 1982: the norm of the Beurling--Ahlfors transform is if , and if .
On quasiconformal dimension distortion for subsets of the real line
Petteri Nissinen, István Prause
Optimal quasiconformal dimension distortions bounds for subsets of the complex plane have been established by Astala. We show that these estimates can be improved when one consider…
On mappings of finite distortion that are quasiconformal in the unit disk
Olli Hirviniemi, Lauri Hitruhin, István Prause +1
We study quasiconformal mappings of the unit disk that have planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the in…
Stretching and Rotation of Planar Quasiconformal Mappings on a Line
Olli Hirviniemi, István Prause, Eero Saksman
In this article, we examine stretching and rotation of planar quasiconformal mappings on a line. We show that for almost every point on the line, the set of complex stretching expo…
Localized Regularity of Planar Maps of Finite Distortion
Olli Hirviniemi, István Prause, Eero Saksman
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the c…
Quasiconformal extensions, Loewner chains, and the lambda-Lemma
Pavel Gumenyuk, István Prause
In 1972, J. Becker [J. Reine Angew. Math. 255] discovered a sufficient condition for quasiconformal extendibility of Loewner chains. Many known conditions for quasiconformal extend…
Quasidisks and twisting of the Riemann map
István Prause
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 in…
Asymptotic variance of the Beurling transform
Kari Astala, Oleg Ivrii, Antti Perälä +1
We study the interplay between infinitesimal deformations of conformal mappings, quasiconformal distortion estimates and integral means spectra. By the work of McMullen, the second…
A hunt for sharp -estimates and rank-one convex variational integrals
Kari Astala, Tadeusz Iwaniec, István Prause +1
Learning how to figure out sharp -estimates of nonlinear differential expressions, to prove and use them, is a fundamental part of the development of PDEs and Geometric Functi…
On a Hölder constant in the theory of quasiconformal mappings
István Prause
A K-quasiconformal selfmap of the unit disk with identity boundary values satisfies the Hölder estimate . The constant i…
Bilipschitz and quasiconformal rotation, stretching and multifractal spectra
Kari Astala, Tadeusz Iwaniec, István Prause +1
We establish sharp bounds for simultaneous local rotation and Hölder-distortion of planar quasiconformal maps. In addition, we give sharp estimates for the corresponding joint quas…
Hausdorff measure of quasicircles
István Prause, Xavier Tolsa, Ignacio Uriarte-Tuero
S. Smirnov proved recently that the Hausdorff dimension of any K-quasicircle is at most 1+k^2, where k=(K-1)/(K+1). In this paper we show that if is such a quasicircle, then $H…
Quasisymmetric distortion spectrum
István Prause, Stanislav Smirnov
We give improved bounds for the distortion of the Hausdorff dimension under quasisymmetric maps in terms of the dilatation of their quasiconformal extension. The sharpness of the e…