Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing geodesic distance for right-invariant Sobolev metrics on
  diffeomorphism groups   We study the geodesic distance induced by right-invariant metrics on the
group $\operatorname{Diff}_\text{c}(M)$ of compactly supported diffeomorphisms,
for various Sobolev norms $W^{s,p}$. Our main result is that the geodesic
distance vanishes identically on every connected component whenever
$s<\min\{n/p,1\}$, where $n$ is the dimension of $M$. We also show that
previous results imply that whenever $s > n/p$ or $s \ge 1$, the geodesic
distance is always positive. In particular, when $n\ge 2$, the geodesic
distance vanishes if and only if $s<1$ in the Riemannian case $p=2$, contrary
to a conjecture made in Bauer et al. [BBHM13].

20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics