Jonas Azzam

activity

20092025

most citedA new characterization of chord-arc domains

69 citations · 285 across the 26 of their papers we have counts for

collaborators

Showing 2014Show all

5 papers · 1 filter

math.MG2014★ 1 cited

Wasserstein Distance and the Rectifiability of Doubling Measures: Part II

Jonas Azzam, Guy David, Tatiana Toro

We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $L^{1}$ Wasserstein distance. We sho…

math.CA2014

Sets of absolute continuity for harmonic measure in NTA domains

Jonas Azzam

We show that if $Ω$ is an NTA domain with harmonic measure $w$ and $E \subseteq \partial Ω$ is contained in an Ahlfors regular set, then $w ∣_{E} ≪ H^{d} ∣_{E}$ . Moreover, t…

math.CA2014

Wasserstein Distance and the Rectifiability of Doubling Measures: Part I

Jonas Azzam, Guy David, Tatiana Toro

Let $μ$ be a doubling measure in $R^{n}$ . We investigate quantitative relations between the rectifiability of $μ$ and its distance to flat measures. More precisely, for $x$ …

math.CA2014★ 69 cited

A new characterization of chord-arc domains

Jonas Azzam, Steve Hofmann, José María Martell +2

We show that if $Ω \subset R^{n + 1}$ , $n \geq 1$ , is a uniform domain (aka 1-sided NTA domain), i.e., a domain which enjoys interior Corkscrew and Harnack Chain conditions, t…

math.CA2014★ 4 cited

Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps

Jonas Azzam, Matthew Badger, Tatiana Toro

A quasiplane $f (V)$ is the image of an $n$ -dimensional Euclidean subspace $V$ of $R^{N}$ ( $1 \leq n \leq N - 1$ ) under a quasiconformal map $f : R^{N} \to R^{N}$ . We give s…