Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pansu pullback and exterior differentiation for Sobolev maps on Carnot
  groups   We show that in an $m$-step Carnot group, a probability measure with finite
$m^{th}$ moment has a well-defined Buser-Karcher center-of-mass, which is a
polynomial in the moments of the measure, with respect to exponential
coordinates. Using this, we improve the main technical result of our previous
paper concerning Sobolev mappings between Carnot groups; as a consequence, a
number of rigidity and structural results from recent papers hold under weaker
assumptions on the Sobolev exponent. We also give applications to quasiregular
mappings, extending earlier work in the $2$-step case to general Carnot groups.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an