Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $C^0$-coerciveness of Moser's problem and smoothing area preserving
  homeomorphisms   In this paper, we establish the $C^0$-coerciveness of Moser's problem of
mapping one smooth volume form to another in terms of the weak topology of
measures associated to the volume forms. The proof relies on our analysis of
Dacorogna-Moser's solution to Moser's problem of mapping one volume form to the
other with the same total mass. As an application, we give a proof of smoothing
result of area preserving homeomorphisms and its parametric version in two
dimension, (or more generally in any dimension in which the smoothing theorem
of homeomorphisms is possible, e.g., in dimension 3 but not necessarily in
dimension 4). This in turn results in coincidence of the area-preserving
homeomorphism group and the symplectic homeomorphism group in two dimension.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio