Tuomas Orponen

activity

20102026

most citedOn restricted families of projections in R^3

52 citations · 367 across the 81 of their papers we have counts for

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4 papers · 1 filter

math.DS2018

Absolute continuity in families of parametrised non-homogeneous self-similar measures

Antti Käenmäki, Tuomas Orponen

Let $μ$ be a planar self-similar measure with similarity dimension exceeding $1$ , satisfying a mild separation condition, and such that the fixed points of the associated similitud…

math.DS2013★ 7 cited

On the packing measure of slices of self-similar sets

Tuomas Orponen

Let $K \subset R^{2}$ be a rotation and reflection free self-similar set satisfying the strong separation condition, with dimension $dim K = s > 1$ . Intersecting $K$ with…

math.DS2012★ 4 cited

On the packing measure of self-similar sets

Tuomas Orponen

Building on a recent result of M. Hochman, we give an example of a linear self-similar set K such that 0 < dim K = s < 1 and P^s(K) = 0. This answers a question of Y. Peres and B.…

math.DS2011

On the Distance Sets of Self-Similar Sets

Tuomas Orponen

We show that if K is a self-similar set in the plane with positive length, then the distance set of K has Hausdorff dimension one.