9 citations · 19 across the 4 of their papers we have counts for
5 papers · 1 filter
Hausdorff dimension of Besicovitch sets of Cantor graphs
Iqra Altaf, Marianna Csörnyei, Kornélia Héra
We consider the Hausdorff dimension of planar Besicovitch sets for rectifiable sets , i.e. sets that contain a rotated copy of in each direction. We show that for a large cl…
Hausdorff dimension of Furstenberg-type sets associated to families of affine subspaces
Kornélia Héra
We show that if and is a nonempty collection of -dimensional affine subspaces of such that every intersects…
The Kakeya problem for circular arcs
Kornélia Héra, Miklós Laczkovich
We prove that if a circular arc has angle short enough, then it can be continuously moved to any prescribed position within a set of arbitrarily small area.
Closed sets with the Kakeya property
Marianna Csörnyei, Kornélia Héra, Miklós Laczkovich
We say that a planar set has the Kakeya property if there exist two different positions of such that can be continuously moved from the first position to the second wit…
Small unions of affine subspaces and skeletons via Baire category
Alan Chang, Marianna Csörnyei, Kornélia Héra +1
Our aim is to find the minimal Hausdorff dimension of the union of scaled and/or rotated copies of the -skeleton of a fixed polytope centered at the points of a given set. For m…