We consider metrics on Euclidean domains $\Omega\subset\R^n$ that are induced
by continuous densities $\rho\colon\Omega\rightarrow(0,\infty)$ and study the
Hausdorff and packing dimensions of the boundary of $\Omega$ with respect to
these metrics.Comment: 20 pages, 2 figure

Klén, Riku

Suomala, Ville

English

arXiv

We consider metrics on Euclidean domains $\Omega\subset\mathbf{R}^n$ that are induced by continuous densities $\rho\colon\Omega\rightarrow(0,\infty)$ and study the Hausdorff and packing dimensions of the boundary of $\Omega$ with respect to these metrics

Dimension of the boundary in different metrics

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