Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tangent spaces of the Teichm{\"u}ller space of the torus with Thurston's
  weak metric   In this paper, we show that the analogue of Thurston's asymmetric metric on
the Teichm{\"u}ller space of flat structures on the torus is weak Finsler and
we give a geometric description of its unit sphere at each point in the tangent
space to Teichm{\"u}ller space. We then introduce a family of weak Finsler
metrics which interpolate between Thurston's asymmetric metric and the
Teichm{\"u}ller metric of the torus (which coincides with the the hyperbolic
metric). We describe the infinitesimal unit spheres of the metrics in this
family.The final version of this paper will appear in Annales Academi\ae \
Scientiarum Fennic\ae \ Mathematica.

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The categories of this paper are: atom-ph
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th