68 citations · 315 across the 32 of their papers we have counts for
36 papers
On the Marstrand projection theorem for the Assouad spectrum
Kenneth J. Falconer, Jonathan M. Fraser, Antti Käenmäki
Marstrand's projection theorem states that the Hausdorff dimension of the orthogonal projection of a Borel set in the plane onto lines is constant almost surely. This property exte…
Level sets of prevalent Weierstrass functions
Zoltán Buczolich, Antti Käenmäki, Balázs Maga
The -Weierstrass function is defined as , where is a Lipschitz function on the unit circle. For a prevalent -Weierstr…
Self-affine sponges with random contractions
Balázs Bárány, Antti Käenmäki, Michał Rams
We compute the almost sure Hausdorff dimension of random self-affine sponges in without imposing any separation conditions. In this context, randomness arises from t…
Thermodynamic formalism of countably generated self-affine sets
Antti Käenmäki, Ian D. Morris
In this article, we further develop the thermodynamic formalism of affine iterated function systems with countably many transformations by showing the existence and extending earli…
Level sets of prevalent Hölder functions
Roope Anttila, Balázs Bárány, Antti Käenmäki
We study the level sets of prevalent Hölder functions. For a prevalent -Hölder function on the unit interval, we show that the upper Minkowski dimension of every level set is bo…
Local dimension spectrum for dominated planar self-affine sets
Alex Batsis, Antti Käenmäki, Tom Kempton
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this…
Tangents of invariant sets
Antti Käenmäki, Alex Rutar
We study the fine scaling properties of sets satisfying various weak forms of invariance. For general attractors of possibly overlapping bi-Lipschitz iterated function systems, we…
Scaling limits of self-conformal measures
Balázs Bárány, Antti Käenmäki, Aleksi Pyörälä +1
We show that any self-conformal measure on is uniformly scaling and generates an ergodic fractal distribution. This generalizes existing results by removing the ne…
Finer geometry of planar self-affine sets
Balázs Bárány, Antti Käenmäki, Han Yu
For planar self-affine sets satisfying the strong separation condition, recent work of Bárány, Hochman, and Rapaport gives mild assumptions under which the Hausdorff dimension equa…
Super-exponential condensation without exact overlaps
Balázs Bárány, Antti Käenmäki
We exhibit self-similar sets on the line which are not exponentially separated and do not generate any exact overlaps. Our result shows that the exponential separation, introduced…
Assouad dimension of planar self-affine sets
Balázs Bárány, Antti Käenmäki, Eino Rossi
We calculate the Assouad dimension of a planar self-affine set satisfying the strong separation condition and the projection condition and show that is minimal for the conf…
Absolute continuity in families of parametrised non-homogeneous self-similar measures
Antti Käenmäki, Tuomas Orponen
Let be a planar self-similar measure with similarity dimension exceeding , satisfying a mild separation condition, and such that the fixed points of the associated similitud…
Attainable values for the Assouad dimension of projections
Jonathan M. Fraser, Antti Käenmäki
We prove that for an arbitrary upper semi-continuous function there exists a compact set in the plane such that for all…
On the Hausdorff dimension of microsets
Jonathan M. Fraser, Douglas C. Howroyd, Antti Käenmäki +1
We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dime…
Birkhoff and Lyapunov spectra on planar self-affine sets
Balázs Bárány, Thomas Jordan, Antti Käenmäki +1
Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spect…
Self-conformal sets with positive Hausdorff measure
Jasmina Angelevska, Antti Käenmäki, Sascha Troscheit
We investigate the Hausdorff measure and content on a class of quasi self-similar sets that include, for example, graph-directed and sub self-similar and self-conformal sets. We sh…
Dynamics of the scenery flow and conical density theorems
Antti Käenmäki
Conical density theorems are used in the geometric measure theory to derive geometric information from given metric information. The idea is to examine how a measure is distributed…
On self-affine sets
Antti Käenmäki
We survey the dimension theory of self-affine sets for general mathematical audience. The article is in Finnish.
Scenery flow, conical densities, and rectifiability
Antti Käenmäki
We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also rev…
Upper Conical density results for general measures on
Marianna Csörnyei, Antti Käenmäki, Tapio Rajala +1
We study conical density properties of general Borel measures on Euclidean spaces. Our results are analogous to the previously known result on the upper density properties of Hausd…
Porosity and regularity in metric measure spaces
Antti Käenmäki
This is a report of a joint work with E. Järvenpää, M. Järvenpää, T. Rajala, S. Rogovin, and V. Suomala. In [3], we characterized uniformly porous sets in -regular metric spaces…
Separation conditions on controlled Moran constructions
Antti Käenmäki, Markku Vilppolainen
It is well known that the open set condition and the positivity of the -dimensional Hausdorff measure are equivalent on self-similar sets, where is the zero of the topologic…
Conical upper density theorems and porosity of measures
Antti Käenmäki, Ville Suomala
We study how measures with finite lower density are distributed around -planes in small balls in . We also discuss relations between conical upper density theo…
Geometric rigidity of a class of fractal sets
Antti Käenmäki
We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of th…