Ville Suomala

activity

20102021

most citedPacking dimension and Ahlfors regularity of porous sets in metric spaces

44 citations · 175 across the 26 of their papers we have counts for

collaborators

Showing math.CAShow all

24 papers · 1 filter

math.CA2021

New bounds on Cantor maximal operators

Pablo Shmerkin, Ville Suomala

We prove $L^{p}$ bounds for the maximal operators associated to an Ahlfors-regular variant of fractal percolation. Our bounds improve upon those obtained by I. Łaba and M. Pramanik a…

math.CA2020

Covering the Sierpiński carpet with tubes

Aleksi Pyörälä, Pablo Shmerkin, Ville Suomala +1

We show that non-trivial $\times N$ -invariant sets in $[0, 1]^{d}$ , such as the Sierpiński carpet and the Sierpiński sponge, are tube-null, that is, they can be covered by a union of…

math.CA2020

Intermediate value property for the Assouad dimension of measures

Ville Suomala

Hare, Mendivil, and Zuberman have recently shown that if $X$ is a compact subset of the reals and of non-zero Assouad dimension $dim_{A} X$ , then for all $s > dim_{A} X$ , $X$ supports…

math.CA2019

Fractal percolation and quasisymmetric mappings

Eino Rossi, Ville Suomala

We study the conformal dimension of fractal percolation and show that, almost surely, the conformal dimension of a fractal percolation is strictly smaller than its Hausdorff dimens…

math.CA2017

Hausdorff dimension of limsup sets of random rectangles in products of regular spaces

Fredrik Ekström, Esa Järvenpää, Maarit Järvenpää +1

The almost sure Hausdorff dimension of the limsup set of randomly distributed rectangles in a product of Ahlfors regular metric spaces is computed in terms of the singular value fu…

math.CA2017★ 8 cited

Upper Conical density results for general measures on $R^{n}$

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…

math.CA2017★ 44 cited

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +3

Let $X$ be a metric measure space with an $s$ -regular measure $μ$ . We prove that if $A \subset X$ is $ϱ$ -porous, then $dim_{p} (A) \leq s - c ϱ^{s}$ where $\dim_{\math…

math.CA2017★ 23 cited

Conical upper density theorems and porosity of measures

Antti Käenmäki, Ville Suomala

We study how measures with finite lower density are distributed around $(n - m)$ -planes in small balls in $R^{n}$ . We also discuss relations between conical upper density theo…

math.CA2017★ 1 cited

Asymptotically sharp dimension estimates for $k$ -porous sets

Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki +1

In $R^{n}$ , we establish an asymptotically sharp upper bound for the upper Minkowski dimension of $k$ -porous sets having holes of certain size near every point in $k$ orthog…

math.CA2016

A class of random Cantor measures, with applications

Pablo Shmerkin, Ville Suomala

We survey some of our recent results on the geometry of spatially independent martingales, in a more concrete setting that allows for shorter, direct proofs, yet is general enough…

math.CA2015★ 4 cited

Dimensions of random covering sets in Riemann manifolds

De-Jun Feng, Esa Järvenpää, Maarit Järvenpää +1

Let $M$ , $N$ and $K$ be $d$ -dimensional Riemann manifolds. Assume that $A := (A_{n})_{n \in N}$ is a sequence of Lebesgue measurable subsets of ${\pmb M…

math.CA2015★ 12 cited

Local dimensions in Moran constructions

Antti Käenmäki, Bing Li, Ville Suomala

We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and $L^{q}$ -dimensions. We generalize and…

math.CA2014

Spatially independent martingales, intersections, and applications

Pablo Shmerkin, Ville Suomala

We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as speci…

math.CA2013

Projections of random covering sets

Changhao Chen, Henna Koivusalo, Bing Li +1

We show that, almost surely, the Hausdorff dimension $s_{0}$ of a random covering set is preserved under all orthogonal projections to linear subspaces with dimension $k > s_{0}$ . The re…

math.CA2013

A note on the hitting probabilities of random covering sets

Bing Li, Ville Suomala

Let $E = n \to \infty lim sup (g_{n} + ξ_{n})$ be the random covering set on the torus $T^{d}$ , where ${g_{n}}$ is a sequence of ball-like sets and $ξ_{n}$ is a sequence of inde…

math.CA2012★ 9 cited

Local multifractal analysis in metric spaces

Antti Käenmäki, Tapio Rajala, Ville Suomala

We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifracta…

math.CA2012

On Cantor sets and doubling measures

Marianna Csörnyei, Ville Suomala

For a large class of Cantor sets on the real-line, we find sufficient and necessary conditions implying that a set has positive (resp. null) measure for all doubling measures of th…

math.CA2012★ 1 cited

Local conical dimensions for measures

De-Jun Feng, Antti Käenmäki, Ville Suomala

We study the decay of $μ (B (x, r) \cap C) / μ (B (x, r))$ as $r ↓ 0$ for different kinds of measures $μ$ on $R^{n}$ and various cones $C$ around $x$ . As an application, we provide s…

math.CA2012★ 5 cited

Sets which are not tube null and intersection properties of random measures

Pablo Shmerkin, Ville Suomala

We show that in $R^{d}$ there are purely unrectifiable sets of Hausdorff (and even box counting) dimension $d - 1$ which are not tube null, settling a question of Carbery, Sor…

math.CA2011★ 5 cited

Dimension, entropy, and the local distribution of measures

Tuomas Sahlsten, Pablo Shmerkin, Ville Suomala

We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generaliz…

math.CA2011

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…

math.CA2010★ 41 cited

Existence of doubling measures via generalised nested cubes

Antti Käenmäki, Tapio Rajala, Ville Suomala

Working on doubling metric spaces, we construct generalised dyadic cubes adapting ultrametric structure. If the space is complete, then the existence of such cubes and the mass dis…

math.CA2010

Dimension of the boundary in different metrics

Riku Klén, Ville Suomala

We consider metrics on Euclidean domains $Ω \subset R^{n}$ that are induced by continuous densities $ρ : Ω \to (0, \infty)$ and study the Hausdorff and packing dimensions of t…

math.CA2010★ 6 cited

Local homogeneity and dimensions of measures

Antti Käenmäki, Tapio Rajala, Ville Suomala

We introduce two new concepts, local homogeneity and local L^q-spectrum, both of which are tools that can be used in studying the local structure of measures. The main emphasis is…

New bounds on Cantor maximal operators

Covering the Sierpiński carpet with tubes

Intermediate value property for the Assouad dimension of measures

Fractal percolation and quasisymmetric mappings

Hausdorff dimension of limsup sets of random rectangles in products of regular spaces

Upper Conical density results for general measures on Rn

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Conical upper density theorems and porosity of measures

Asymptotically sharp dimension estimates for k-porous sets

A class of random Cantor measures, with applications

Dimensions of random covering sets in Riemann manifolds

Local dimensions in Moran constructions

Spatially independent martingales, intersections, and applications

Projections of random covering sets

A note on the hitting probabilities of random covering sets

Local multifractal analysis in metric spaces

On Cantor sets and doubling measures

Local conical dimensions for measures

Sets which are not tube null and intersection properties of random measures

Dimension, entropy, and the local distribution of measures

Thin and fat sets for doubling measures in metric spaces

Existence of doubling measures via generalised nested cubes

Dimension of the boundary in different metrics

Local homogeneity and dimensions of measures

Upper Conical density results for general measures on $R^{n}$

Asymptotically sharp dimension estimates for $k$ -porous sets