Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$-moduli spaces of symplectic vortices on Riemann surfaces with
  cylindrical ends   Let $(X,\omega)$ be a compact symplectic manifold with a Hamiltonian action
of a compact Lie group $G$ and $\mu: X\to \mathfrak g$ be its moment map. In
this paper, we study the $L^2$-moduli spaces of symplectic vortices on Riemann
surfaces with cylindrical ends. We studied a circle-valued action functional
whose gradient flow equation corresponds to the symplectic vortex equations on
a cylinder $S^1\times \mathbb R$. Assume that $0$ is a regular value of the
moment map $\mu$, we show that the functional is of Bott-Morse type and its
critical points of the functional form twisted sectors of the symplectic
reduction (the symplecitc orbifold $[\mu^{-1}(0)/G]$).
  We show that any gradient flow lines approaches its limit point exponentially
fast. Fredholm theory and compactness property are then established for the
$L^2$-Moduli spaces of symplectic vortices on Riemann surfaces with cylindrical
ends.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex