Katrin Fassler

activity

20162026

most citedRiesz transform and vertical oscillation in the Heisenberg group

10 citations · 18 across the 10 of their papers we have counts for

collaborators

12 papers

math.MG2026

On low-dimensional uniform rectifiability in Heisenberg groups

Katrin Fässler, Andrea Pinamonti, Kilian Zambanini

Refining an earlier result due to Hahlomaa, we provide a new Carleson-type condition for $k$ -regular sets in the Heisenberg group $H^{n}$ to have big pieces of Lipschitz ima…

math.MG2025

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2

Katrin Fässler, Ivan Yuri Violo

We characterize uniform $k$ -rectifiability in Euclidean spaces in terms of a Carleson-type geometric lemma for a new notion of flatness coefficients, which we call $ι$ -numbers. The…

math.MG2023

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 1

Katrin Fässler, Ivan Yuri Violo

We introduce new flatness coefficients, which we call $ι$ -numbers, for Ahlfors $k$ -regular sets in metric spaces ( $k \in N$ ). Using these coefficients for $k = 1$ , we charact…

math.CA2023★ 1 cited

On the Hausdorff dimension of circular Furstenberg sets

Katrin Fässler, Jiayin Liu, Tuomas Orponen

For $0 \leq s \leq 1$ and $0 \leq t \leq 3$ , a set $F \subset R^{2}$ is called a circular $(s, t)$ -Furstenberg set if there exists a family of circles $S$ of Haus…

math.CA2022★ 3 cited

A note on Kakeya sets of horizontal and $S L (2)$ lines

Katrin Fässler, Tuomas Orponen

We consider unions of $S L (2)$ lines in $R^{3}$ . These are lines of the form $L = (a, b, 0) + span (c, d, 1),$ where $a d - b c = 1$ . We show that if $L$ is a…

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.CA2019

Singular integrals on regular curves in the Heisenberg group

Katrin Fässler, Tuomas Orponen

Let $H$ be the first Heisenberg group, and let $k \in C^{\infty} (H ∖ {0})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\…

math.CA2019★ 3 cited

Metric rectifiability of $H$ -regular surfaces with Hölder continuous horizontal normal

Daniela Di Donato, Katrin Fässler, Tuomas Orponen

Two definitions for the rectfiability of hypersurfaces in Heisenberg groups $H^{n}$ have been proposed: one based on $H$ -regular surfaces, and the other on Lipschit…

math.CA2018★ 10 cited

Riesz transform and vertical oscillation in the Heisenberg group

Katrin Fässler, Tuomas Orponen

We study the $L^{2}$ -boundedness of the $3$ -dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $H$ . Inspired by the notio…

math.CA2018

Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group

Katrin Fässler, Tuomas Orponen, Séverine Rigot

A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. E…

math.CA2016

Intrinsic Lipschitz graphs and vertical $β$ -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 $H$ . In particular, we aim to demonstr…

math.CA2016

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 $R^{2}$ of length one. The classical "worm problem" of L.…

On low-dimensional uniform rectifiability in Heisenberg groups

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2

On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 1

On the Hausdorff dimension of circular Furstenberg sets

A note on Kakeya sets of horizontal and SL(2) lines

Planar incidences and geometric inequalities in the Heisenberg group

Singular integrals on regular curves in the Heisenberg group

Metric rectifiability of H-regular surfaces with Hölder continuous horizontal normal

Riesz transform and vertical oscillation in the Heisenberg group

Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group

Intrinsic Lipschitz graphs and vertical β-numbers in the Heisenberg group

Curve packing and modulus estimates

A note on Kakeya sets of horizontal and $S L (2)$ lines

Metric rectifiability of $H$ -regular surfaces with Hölder continuous horizontal normal

Intrinsic Lipschitz graphs and vertical $β$ -numbers in the Heisenberg group