Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Length spectral rigidity of non-positively curved surfaces   Length spectral rigidity is the question of under what circumstances the
geometry of a surface can be determined, up to isotopy, by knowing only the
lengths of its closed geodesics. It is known that this can be done for
negatively curved Riemannian surfaces, as well as for negatively-curved cone
surfaces. Steps are taken toward showing that this holds also for flat cone
surfaces, and it is shown that the lengths of closed geodesics are also enough
to determine which of these three categories a geometric surface falls into.
Techniques of Gromov, Bonahon, and Otal are explained and adapted, such as
topological conjugacy, geodesic currents, Liouville measures, and the average
angle between two geometric surfaces.

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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th