52 citations · 367 across the 81 of their papers we have counts for
7 papers · 2 filters
On the dimension of visible parts
Tuomas Orponen
I prove that the visible parts of a compact set in , , have Hausdorff dimension at most from almost every direction.
Singular integrals on regular curves in the Heisenberg group
Katrin Fässler, Tuomas Orponen
Let be the first Heisenberg group, and let be a kernel which is either odd or horizontally odd, and satisfies $$|\…
Metric rectifiability of -regular surfaces with Hölder continuous horizontal normal
Daniela Di Donato, Katrin Fässler, Tuomas Orponen
Two definitions for the rectfiability of hypersurfaces in Heisenberg groups have been proposed: one based on -regular surfaces, and the other on Lipschit…
Vertical versus horizontal Sobolev spaces
Katrin Fässler, Tuomas Orponen
Let , , and let be the Heisenberg group. Folland in 1975 showed that if is a function in the hori…
Quantitative absolute continuity of planar measures with two independent Alberti representations
David Bate, Tuomas Orponen
We study measures on the plane with two independent Alberti representations. It is known, due to Alberti, Csörnyei, and Preiss, that such measures are absolutely continuous wit…
On the Assouad dimension of projections
Tuomas Orponen
Let , and let stand for Assouad dimension. I prove that for all $e \in…