19 citations · 21 across the 6 of their papers we have counts for
7 papers
Area-filling curves
Maria Chiara Nasso, Aljoša Volčič
In this paper we study area-filling curves, i.e. continuous and injective mappings defined on [0,1] whose graph has positive measure. Current literature calls them ``Osgood curves"…
A dynamical system approach to the Kakutani-Fibonacci sequence
Ingrid Carbone, Maria Rita Iacò, Aljoša Volčič
In this paper we consider the sequence of Kakutani's -refinements corresponding to the inverse of golden ratio (which we call Kakutani-Fibonacci sequence of partitions) and asso…
Convergence in shape of Steiner symmetrizations
Gabriele Bianchi, Almut Burchard, Paolo Gronchi +1
There are sequences of directions such that, given any compact set K in R^n, the sequence of iterated Steiner symmetrals of K in these directions converges to a ball. However examp…
Uniform distribution on the sphere and caps
Aljosa Volcic
In this note we will consider the question when from the appropriate behavior of a sequence of points on caps we can conclude that the sequence is uniformly distributed on the sphe…
Random symmetrizations of measurable sets
Aljosa Volcic
In this paper we prove almost sure convergence to the ball, in the Nikodym metric, of sequences of random Steiner symmetrizations of bounded Caccioppoli and bounded measurable sets…
A generalization of Kakutani's splitting procedure
Aljosa Volcic
In this paper we will study uniformly distributed sequences of partitions of [0,1], a concept which has been introduced by Kakutani in 1976. We will construct new families of u.d.…