Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BiLipschitz embeddings of spheres into jet space Carnot groups not
  admitting Lipschitz extensions   For all $k,n\ge 1$, we construct a biLipschitz embedding of $\mathbb{S}^n$
into the jet space Carnot group $J^k(\mathbb{R}^n)$ that does not admit a
Lipschitz extension to $\mathbb{B}^{n+1}$. Let $f:\mathbb{B}^n\to \mathbb{R}$
be a smooth, positive function with $k^{th}$-order derivatives that are
approximately linear near $\partial \mathbb{B}^n$. The embedding is given by
taking the jet of $f$ on the upper hemisphere and the jet of $-f$ on the lower
hemisphere, where we view $\mathbb{S}^n$ as two copies of $\mathbb{B}^n$. To
prove the lack of a Lipschitz extension, we apply a factorization result of
Wenger and Young for $n=1$ and modify an argument of Rigot and Wenger for $n\ge
2$.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph