Ying-Ying Cai

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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…

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

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