Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy distribution of harmonic 1-forms and Jacobians of Riemann
  surfaces with a short closed geodesic   We study the energy distribution of harmonic 1-forms on a compact hyperbolic
Riemann surface $S$ where a short closed geodesic is pinched. If the geodesic
separates the surface into two parts, then the Jacobian torus of $S$ develops
into a torus that splits. If the geodesic is nonseparating then the Jacobian
torus of $S$ degenerates. The aim of this work is to get insight into this
process and give estimates in terms of geometric data of both the initial
surface $S$ and the final surface, such as its injectivity radius and the
lengths of geodesics that form a homology basis. As an invariant we introduce
new families of symplectic matrices that compensate for the lack of full
dimensional Gram-period matrices in the noncompact case.

19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph