Dimension of the boundary in different metrics

preprint2012arXivOpen access

We consider metrics on Euclidean domains $Ω\subset\R^n$ that are induced by continuous densities $ρ\colonΩ\rightarrow(0,\infty)$ and study the Hausdorff and packing dimensions of the boundary of $Ω$ with respect to these metrics.

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Dimension of the boundary in different metrics

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