21 citations · 22 across the 7 of their papers we have counts for
4 papers · 1 filter
Rigidity of quasisymmetric mappings on self-affine carpets
Antti Käenmäki, Tuomo Ojala, Eino Rossi
We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this cas…
A function whose graph has positive doubling measure
Tuomo Ojala, Tapio Rajala
We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen. Moreover we show that th…
On -regular sets
Tuomo Ojala
We define -regular sets in uniformly perfect metric spaces. This definition is quasisymmetrically invariant and the construction resembles generalized dyadic cubes in metri…
Thin and fat sets for doubling measures in metric spaces
Tuomo Ojala, Tapio Rajala, Ville Suomala
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are…