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

Issue

Vol. 97 No. 2 (2005)

Section

Articles

How to Cite

[1]
E. Järvenpää, M. Järvenpää, A. Käenmäki, and V. Suomala, “Asymptotically sharp dimension estimates for $k$-porous sets”, Math. Scand., vol. 97, no. 2, pp. 309–318, Dec. 2005, doi: 10.7146/math.scand.a-14978.