Displaying similar documents to “Harmonic measures versus quasiconformal measures for hyperbolic groups”

Optimal transportation for multifractal random measures and applications

Rémi Rhodes, Vincent Vargas (2013)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metrics, the volume forms of which coincide with the multifractal random measures.

Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Paweł Płonka (2016)

Annales Mathematicae Silesianae

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In this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in [6], that is showing it using conditions generalizing the notion of tightness of measures. In order to do that we use tightness theory for random measures as developed by H. Crauel in [2].

Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings

David Kalaj (2011)

Studia Mathematica

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We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.

Harmonic mappings in the exterior of the unit disk

Jarosław Widomski, Magdalena Gregorczyk (2010)

Annales UMCS, Mathematica

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In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition [...] . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.