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Sous-ensembles de courbes Ahlfors-régulières et nombres de Jones.

Hervé Pajot (1996)

Publicacions Matemàtiques

We prove that an Ahlfors-regular set (with dimension one) E ⊂ Rn which verifies a βq-version of P. W. Jones' geometric lemma is included in an Ahlfors-regular curve Γ.This theorem is due to G. David and S. Semmes, we give a more direct proof.

Spirallike mappings and univalent subordination chains in n

Ian Graham, Hidetaka Hamada, Gabriela Kohr, Mirela Kohr (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we consider non-normalized univalent subordination chains and the connection with the Loewner differential equation on the unit ball in n . To this end, we study the most general form of the initial value problem for the transition mapping, and prove the existence and uniqueness of solutions. Also we introduce the notion of generalized spirallikeness with respect to a measurable matrix-valued mapping, and investigate this notion from the point of view of non-normalized univalent subordination...

Squeezing the Sierpinski sponge

Tadeusz Iwaniec, Gaven Martin (2002)

Studia Mathematica

We give an example relating to the regularity properties of mappings with finite distortion. This example suggests conditions to be imposed on the distortion function in order to avoid "cavitation in measure".

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