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.

Full Text:




  • There are currently no refbacks.
This website uses cookies to allow us to see how the site is used. The cookies cannot identify you or any content at your own computer.

ISSN 0025-5521 (print) ISSN 1903-1807 (online)

Hosted by The State and University Library