Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pliability, or the whitney extension theorem for curves in carnot groups   The Whitney extension theorem is a classical result in analysis giving a
necessary and sufficient condition for a function defined on a closed set to be
extendable to the whole space with a given class of regularity. It has been
adapted to several settings, among which the one of Carnot groups. However, the
target space has generally been assumed to be equal to R^d for some d $\ge$ 1.
We focus here on the extendability problem for general ordered pairs
(G\_1,G\_2) (with G\_2 non-Abelian). We analyze in particular the case G\_1 = R
and characterize the groups G\_2 for which the Whitney extension property
holds, in terms of a newly introduced notion that we call pliability.
Pliability happens to be related to rigidity as defined by Bryant an Hsu. We
exploit this relation in order to provide examples of non-pliable Carnot
groups, that is, Carnot groups so that the Whitney extension property does not
hold. We use geometric control theory results on the accessibility of control
affine systems in order to test the pliability of a Carnot group. In
particular, we recover some recent results by Le Donne, Speight and Zimmermann
about Lusin approximation in Carnot groups of step 2 and Whitney extension in
Heisenberg groups. We extend such results to all pliable Carnot groups, and we
show that the latter may be of arbitrarily large step.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
7
The categories of this paper are: hep-th