Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bi-Lipschitz embeddings of $SRA$-free spaces into Euclidean spaces   $SRA$-free spaces is a wide class of metric spaces including finite
dimensional Alexandrov spaces of non-negative curvature, complete Berwald
spaces of nonnegative flag curvature, Cayley Graphs of virtually abelian groups
and doubling metric spaces of non-positive Busemann curvature with extendable
geodesics. This class also includes arbitrary big balls in complete, locally
compact $CAT(k)$-spaces $(k \in \mathbb R)$ with locally extendable geodesics,
finite-dimensional Alexandrov spaces of curvature $\ge k$ with $k \in R$ and
complete Finsler manifolds satisfying the doubling condition.
  We show that $SRA$-free spaces allow bi-Lipschitz embeddings in Euclidean
spaces. As a corollary we obtain a quantitative bi-Lipschitz embedding theorem
for balls in finite dimensional Alexandrov spaces of curvature bounded from
below conjectured by S. Eriksson-Bique.
  The main tool of the proof is an extension theorem for bi-Lipschitz maps into
Euclidean spaces. This extension theorem is close in nature with the embedding
theorem of J. Seo and may be of independent interest.

19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
29
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: q-fin
36
The categories of this paper are: cmp-lg