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arXiv · 1701.08584

Asymptotically sharp dimension estimates for $k$-porous sets

Esa Järvenpää·Maarit Järvenpää·Antti Käenmäki·Ville Suomala
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Abstract

In $\mathbb{R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimension of $k$-porous sets having holes of certain size near every point in $k$ orthogonal directions at all small scales. This bound tends to $n-k$ as $k$-porosity tends to its maximum value.

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Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki, Ville Suomala. 2017-01-30. Asymptotically sharp dimension estimates for $k$-porous sets. https://arxiv.org/abs/1701.08584

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