Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure of Porous Sets in Carnot Groups   We show that any Carnot group contains a closed nowhere dense set which has
measure zero but is not $\sigma$-porous with respect to the
Carnot-Carath\'eodory (CC) distance. In the first Heisenberg group we observe
that there exist sets which are porous with respect to the CC distance but not
the Euclidean distance and vice-versa. In Carnot groups we then construct a
Lipschitz function which is Pansu differentiable at no point of a given
$\sigma$-porous set and show preimages of open sets under the horizontal
gradient are far from being porous.

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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin