52 citations · 367 across the 81 of their papers we have counts for
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Improving Kaufman's exceptional set estimate for packing dimension
Tuomas Orponen
Given , I prove that there exists a constant such that the following holds. Let be a Borel set with , an…
An improved bound on the packing dimension of Furstenberg sets in the plane
Tuomas Orponen
Let . A set is a Furstenberg -set, if for every unit vector , some line parallel to satisfies $$\dim_{\mathr…
Intrinsic Lipschitz graphs and vertical -numbers in the Heisenberg group
Vasileios Chousionis, Katrin Fässler, Tuomas Orponen
The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group . In particular, we aim to demonstr…
Boundedness of the density normalised Jones' square function does not imply -rectifiability
Henri Martikainen, Tuomas Orponen
Recently, M. Badger and R. Schul proved that for a -rectifiable Radon measure , the density weighted Jones' square function $$ J_{1}(x) = \mathop{\sum_{Q \in \mathcal{D}}}_{\…
A sharp exceptional set estimate for visibility
Tuomas Orponen
A Borel set is visible from , if the radial projection of with base point has positive measure. I pro…
Curve packing and modulus estimates
Katrin Fässler, Tuomas Orponen
A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in of length one. The classical "worm problem" of L.…