Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Whitney's Extension Theorem and the finiteness principle for curves in
  the Heisenberg group   Consider the sub-Riemannian Heisenberg group $\mathbb{H}$. In this paper, we
answer the following question: given a compact set $K \subseteq \mathbb{R}$ and
a continuous map $f:K \to \mathbb{H}$, when is there a horizontal $C^m$ curve
$F:\mathbb{R} \to \mathbb{H}$ such that $F|_K = f$? Whitney originally answered
this question for real valued mappings, and Fefferman provided a complete
answer for real valued functions defined on subsets of $\mathbb{R}^n$. We also
prove a finiteness principle for $C^{m,\sqrt{\omega}}$ horizontal curves in the
Heisenberg group in the sense of Brudnyi and Shvartsman.

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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ
9
The categories of this paper are: nlin