Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability estimates for the conformal group of $\mathbb{S}^{n-1}$ in
  dimension $n\geq 3$   The purpose of this paper is to exhibit a quantitative stability result for
the class of M\"obius transformations of $\mathbb{S}^{n-1}$ when $n\geq 3$. The
main estimate is of local nature and asserts that for a Lipschitz map that is
apriori close to a M\"obius transformation, an average conformal-isoperimetric
type of deficit controls the deviation (in an average sense) of the map in
question from a particular M\"obius map. The optimality of the result together
with its link with the geometric rigidity of the special orthogonal group are
also discussed.

3
The categories of this paper are: physics
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex