Asymptotically sharp dimension estimates for $k$-porous sets | Zendy

Esa Järvenpää | Zendy; Maarit Järvenpää | Zendy; Antti Käenmäki | Zendy; Ville Suomala | Zendy

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Asymptotically sharp dimension estimates for $k$-porous sets

Author(s) -

Esa Järvenpää,

Maarit Järvenpää,

Antti Käenmäki,

Ville Suomala

Publication year - 2005

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.553

H-Index - 30

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-14978

Subject(s) - mathematics , dimension (graph theory) , upper and lower bounds , minkowski space , minkowski–bouligand dimension , combinatorics , porosity , point (geometry) , mathematical analysis , geometry , materials science , fractal dimension , composite material , fractal

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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