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research
Dimension of the boundary in different metrics
Authors
Riku Klén
Ville Suomala
Publication date
25 April 2012
Publisher
View
on
arXiv
Abstract
We consider metrics on Euclidean domains
Ω
⊂
R
n
\Omega\subset\R^n
Ω
⊂
R
n
that are induced by continuous densities
ρ
:
Ω
→
(
0
,
∞
)
\rho\colon\Omega\rightarrow(0,\infty)
ρ
:
Ω
→
(
0
,
∞
)
and study the Hausdorff and packing dimensions of the boundary of
Ω
\Omega
Ω
with respect to these metrics.Comment: 20 pages, 2 figure
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Last time updated on 29/10/2019