Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minkowski content and fractal Euler characteristic for conformal graph
  directed systems   We study the (local) Minkowski content and the (local) fractal Euler
characteristic of limit sets $F\subset\mathbb R$ of conformal graph directed
systems (cGDS) $\Phi$. For the local quantities we prove that the logarithmic
Ces\`aro averages always exist and are constant multiples of the
$\delta$-conformal measure. If $\Phi$ is non-lattice, then also the non-average
local quantities exist and coincide with their respective average versions.
When the conformal contractions of $\Phi$ are analytic, the local versions
exist if and only if $\Phi$ is non-lattice. For the non-local quantities the
above results in particular imply that limit sets of Fuchsian groups of
Schottky type are Minkowski measurable, proving a conjecture of Lapidus from
1993. Further, when the contractions of the cGDS are similarities, we obtain
that the Minkowski content and the fractal Euler characteristic of $F$ exist if
and only if $\Phi$ is non-lattice, generalising earlier results by Falconer,
Gatzouras, Lapidus and van Frankenhuijsen for non-degenerate self-similar
subsets of $\mathbb R$ that satisfy the open set condition.

21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph