Katrin Fassler

activity

20242026

collaborators

4 papers

math.MG2026

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

Katrin FÃ¤ssler, 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 $I^^{1}$ -numbers. Th…

math.MG2026

On low-dimensional uniform rectifiability in Heisenberg groups

Katrin FÃ¤ssler, 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 1

Katrin FÃ¤ssler, Ivan Yuri Violo

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

math.CA2024

On the Hausdorff dimension of circular Furstenberg sets

Katrin FÃ¤ssler, 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…