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 2017 · math.CAShow all

8 papers · 2 filters

math.CA2017★ 4 cited

Improved bounds for restricted families of projections to planes in $R^{3}$

Tuomas Orponen, Laura Venieri

For $e \in S^{2}$ , the unit sphere in $R^{3}$ , let $π_{e}$ be the orthogonal projection to $e^{⊥} \subset R^{3}$ , and let $W \subset R^{3}$ be any $2$ -…

math.CA2017★ 39 cited

On the dimension and smoothness of radial projections

Tuomas Orponen

This paper contains two results on the dimension and smoothness of radial projections of sets and measures in Euclidean spaces. To introduce the first one, assume that $E,K \subset…

math.CA2017

On the absolute continuity of radial projections

Tuomas Orponen

Let $d \geq 2$ and $d - 1 < s < d$ . Let $μ$ be a compactly supported Radon measure in $R^{d}$ with finite $s$ -energy. I prove that the radial projections $π_{x ♯} μ$ of…

math.CA2017

Boundedness of singular integrals on $C^{1, α}$ intrinsic graphs in the Heisenberg group

Vasileios Chousionis, Katrin Fässler, Tuomas Orponen

We study singular integral operators induced by $3$ -dimensional Calderón-Zygmund kernels in the Heisenberg group. We show that if such an operator is $L^{2}$ bounded on vertical pl…

math.CA2017★ 10 cited

A Marstrand-type restricted projection theorem in $R^{3}$

Antti Käenmäki, Tuomas Orponen, Laura Venieri

Marstrand's projection theorem from $1954$ states that if $K \subset R^{3}$ is an analytic set, then, for $H^{2}$ almost every $e \in S^{2}$ , the orthogonal proj…

math.CA2017

Every locally finite Borel measure on $R$ has conformal dimension zero

Tuomas Orponen

A result of P. Tukia from 1989 says that Lebesgue measure on $R$ has conformal dimension zero: for every $ε > 0$ , there is a Borel set $G \subset R$ of full Lebesg…

Improved bounds for restricted families of projections to planes in R3

On the dimension and smoothness of radial projections

On the absolute continuity of radial projections

Boundedness of singular integrals on C1,α intrinsic graphs in the Heisenberg group

A Marstrand-type restricted projection theorem in R3

Every locally finite Borel measure on R has conformal dimension zero

Improved bounds for restricted families of projections to planes in $R^{3}$

Boundedness of singular integrals on $C^{1, α}$ intrinsic graphs in the Heisenberg group

A Marstrand-type restricted projection theorem in $R^{3}$

Every locally finite Borel measure on $R$ has conformal dimension zero