Dimension of the boundary in different metrics (Q2847669)

The authors consider the Hausdorff and packing dimensions of the boundary of Euclidean domains \(\Omega\subset \mathbb{R}^n\) with respect to some metrics that are induced by continuous densities \(\rho:\Omega\rightarrow(0,\infty)\). Although they provide some estimates in the setting of conformal densities, their main goal is to study general densities defined on John domains in \(\mathbb{R}^n\), and to provide suitable tools to estimate the values of the Hausdorff and packing dimensions. For this reason, the methods used throughout the paper are more geometric than analytic.