Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An existence theorem, with energy bounds, of Floer's perturbed
  Cauchy-Riemann equation with jumping discontinuity   This is a sequel to the paper [Oh5] (or ArXiv:math.SG/0206092). The main
purpose of the paper is to give the proof of an existence theorem, with energy
bounds, of certain pseudo-holomorphic sections of the mapping cylinder that is
needed for the proof of nondegeneracy of the homological invariant pseudo-norm
which the author has constructed on general symplectic manifolds [Oh4,5]. The
existence theorem is also the crux of the author's recent proof of an optimal
energy-capacity inequality given in [Oh5]. In this paper, we prove a more
general existence result than needed in that we study Floer's perturbed
Cauchy-Riemann equations with discontinous Hamiltonian perturbation terms and
prove an existence theorem of certain piecewise smooth finite energy solutions
of the equation. The proof relies on a careful study of the product structure
in the chain level Floer homology theory and a singular degeneration
(``adiabatic degeneration'') of Floer's perturbed Cauchy-Riemann equation. In
the course of the proof, we also derive certain general energy identity of
pseudo-holomorphic sections of the Hamiltonian fibration.

16
The categories of this paper are: stat
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph