68 citations · 315 across the 32 of their papers we have counts for
13 papers · 1 filter
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…
Asymptotically sharp dimension estimates for -porous sets
Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +1
In , we establish an asymptotically sharp upper bound for the upper Minkowski dimension of -porous sets having holes of certain size near every point in orthog…
Measures of full dimension on self-affine sets
Antti Käenmäki
Under the assumption of a natural subadditive potential, the so called cylinder function, working on the symbol space we prove the existence of the ergodic invariant probability me…
On natural invariant measures on generalised iterated function systems
Antti Käenmäki
We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the inva…
On the geometric structure of the limit set of conformal iterated function systems
Antti Käenmäki
We consider infinite conformal iterated function systems on . We study the geometric structure of the limit set of such systems. Suppose this limit set intersects som…
On upper conical density results
Antti Käenmäki
We report a recent developement on the theory of upper conical densities. More precicely, we look at what can be said in this respect for other measures than just the Hausdorff mea…