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

collaborators

Showing 2020 · math.CAShow all

5 papers · 2 filters

math.CA2020

Rickman rugs and intrinsic bilipschitz graphs

Tuomas Orponen

This paper studies the geometry of bilipschitz maps $f : W \to H$ , where $H$ is the first Heisenberg group, and $W \subset H$ is a…

math.CA2020★ 9 cited

Plenty of big projections imply big pieces of Lipschitz graphs

Tuomas Orponen

I prove that a closed $n$ -regular set $E \subset R^{d}$ with plenty of big projections has big pieces of Lipschitz graphs. This answers a question of David and Semmes.

math.CA2020

Sub-elliptic boundary value problems in flag domains

Tuomas Orponen, Michele Villa

A flag domain in $R^{3}$ is a subset of $R^{3}$ of the form ${(x, y, t) : y < A (x)}$ , where $A : R \to R$ is a Lipschitz function. We solve…

math.CA2020★ 1 cited

Planar incidences and geometric inequalities in the Heisenberg group

Katrin Fässler, Tuomas Orponen, Andrea Pinamonti

We prove that if $P, L$ are finite sets of $δ$ -separated points and lines in $R^{2}$ , the number of $δ$ -incidences between $P$ and $L$ is no larger than…

math.CA2020★ 5 cited

Combinatorial proofs of two theorems of Lutz and Stull

Tuomas Orponen

Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not a…