2025/05/24 by Akramov, Nurali, Rakhimov, Karim
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.18801
In this work, we prove that the complement of the Brjuno set in ℂn has zero Cσ-capacity with respect to the kernel kσ(z,ξ)=‖z-ξ‖-2n+2|log‖z-ξ‖|σ for any σ>n. In particular, it follows that it has zero hδ-Hausdorff measure with respect to the hδ(t)=t2n-2|logt|-δ, for any δ>n+1. This generalizes a previous result of Sadullaev and the second author in dimension one to higher dimensions.