Asymptotically sharp dimension estimates for $k$-porous sets

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

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.
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
Section
Articles