Asymptotically sharp dimension estimates for $k$-porous sets

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

doi:10.7146/math.scand.a-14978

Asymptotically sharp dimension estimates for $k$-porous sets

Authors

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

DOI:

https://doi.org/10.7146/math.scand.a-14978

Abstract

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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Published

2005-12-01

How to Cite

Järvenpää, E., Järvenpää, M., Käenmäki, A., & Suomala, V. (2005). Asymptotically sharp dimension estimates for $k$-porous sets. MATHEMATICA SCANDINAVICA, 97(2), 309–318. https://doi.org/10.7146/math.scand.a-14978