Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On analysis of the exponential map of volume-preserving diffeomorphism
  group on closed orientable surfaces through the vorticity   We study the exponential map of group of volume-preserving diffeomorphisms on
closed orientable surfaces via the vorticity formulation of the incompressible
Euler equation. We present an alternative, fluid dynamical proof of the theorem
of Ebin--Misio\l{}ek--Preston: the exponential is a nonlinear Fredholm mapping
of index zero. We extend Shnirelman's rigidity result for the exponential map
from 2-dimensional flat torus to arbitrary orientable closed surfaces. That is,
we prove that the exponential map is Fredholm quasiregular.

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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con