Xavier Tolsa

collaborators

4 papers

math.AP2026

Failure of dimension drop for harmonic measure on Ahlfors regular flat boundaries

Yingying Cai, Cole Jeznach, Xavier Tolsa

We develop an $N$ -adic modification of the construction of David-Jeznach-Julia for compact subsets of the real line $R \subset C$ for which harmonic measure for the…

math.AP2026

Failure of dimension drop for harmonic measure on Ahlfors regular boundaries of dimension close to $1$

Yingying Cai, Cole Jeznach, Xavier Tolsa

For every $0 < s < 1$ we construct a compact $s$ -Ahlfors regular set $K \subset C$ for which harmonic measure of $C ∖ K$ with pole at infinity is comparable to $\m…

math.AP2026

Dimension Drop for Harmonic Measure on Ahlfors Regular Boundaries

Yingying Cai, Xavier Tolsa

We provide quantitative estimates for the dimension drop of harmonic measure. We show that for a domain $Ω = R^{n + 1} ∖ E$ where $E$ is an $s$ -Ahlfors regular compac…

math.AP2023

The $A_{\infty}$ condition, $ε$ -approximators, and Varopoulos extensions in uniform domains

Simon Bortz, Bruno Poggi, Olli Tapiola +1

Suppose that $Ω \subset R^{n + 1}$ , $n \geq 1$ , is a uniform domain with $n$ -Ahlfors regular boundary and $L$ is a (not necessarily symmetric) divergence form elliptic, real, bou…

Failure of dimension drop for harmonic measure on Ahlfors regular flat boundaries

Failure of dimension drop for harmonic measure on Ahlfors regular boundaries of dimension close to 1

Dimension Drop for Harmonic Measure on Ahlfors Regular Boundaries

The A∞​ condition, ε-approximators, and Varopoulos extensions in uniform domains

Failure of dimension drop for harmonic measure on Ahlfors regular boundaries of dimension close to $1$

The $A_{\infty}$ condition, $ε$ -approximators, and Varopoulos extensions in uniform domains