On Minkowski dimension of quasicircles

Thanh Hoang Nhat Le (1) , Michel Zinsmeister (1, 2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LPMC - Laboratoire de physique de la matière condensée

In this paper, we give a positive answer for Mc Mullen's open question which addresses a problem of the Hausdorff dimension of quasicircles. We also give a negative answer for this question by constructing a counterexample which is reminiscent of Kahane's construction of a non-Smirnov domain.

Mots clés: Minkowski dimension; Hausdorff dimension; dyadic martingale; Mc Mullen's open question; Bloch function; Kahane's measure

Domaines: Systèmes dynamiques [math.DS]

Thanh Hoang Nhat Le, Michel Zinsmeister. On Minkowski dimension of quasicircles. 2012. ⟨hal-00705005⟩