Asymptotically sharp dimension estimates for $k$-porous sets

E. Järvenpää, M. Järvenpää, A. Käenmäki, V. Suomala


In ${\mathsf R}^n$, 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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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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