Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One-dimensional Gromov minimal filling   The present paper opens a new branch in the theory of variational problems
with branching extremals, the investigation of one-dimensional minimal fillings
of finite pseudo-metric spaces. On the one hand, this problem is a
one-dimensional version of a generalization of Gromov's minimal fillings
problem to the case of stratified manifolds (the filling in our case is a
weighted graph). On the other hand, this problem is interesting in itself and
also can be considered as a generalization of another classical problem,
namely, the Steiner problem on the construction of a shortest network joining a
given set of terminals. Besides the statement of the problem, we discuss
several properties of the minimal fillings, describe minimal fillings of
additive spaces, and state several conjectures. We also include some
announcements concerning the very recent results obtained in our group,
including a formula calculating the weight of the minimal filling for an
arbitrary finite pseudo-metric space and the concept of pseudo-additive space
which generalizes the classical concept of additive space. We hope that the
theory of one-dimensional minimal fillings refreshes the interest in the
Steiner problem and gives an opportunity to solve several long standing
problems, such as the calculation of the Steiner ratio, in particular the
verification of the Gilbert--Pollack conjecture on the Steiner ratio of the
Euclidean plane.

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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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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-bio
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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: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int