Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The large scale geometry of nilpotent Lie groups   In this paper, we prove results concerning the large scale geometry of
connected, simply connected nonabelian nilpotent Lie groups equipped with left
invariant Riemannian metrics. Precisely, we prove that there do not exist
quasi-isometric embeddings of such a nilpotent Lie group into either a CAT(0)
metric space or an Alexandrov metric space with curvature bounded below. The
main technical aspect of this work is the proof of a limited metric
differentiability of Lipschitz maps between connected graded nilpotent Lie
groups equipped with left invariant Carnot-Caratheodory metrics and complete
metric spaces.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex