Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and convergence of the length-preserving elastic flow of
  clamped curves   We study the evolution of curves with fixed length and clamped boundary
conditions moving by the negative $L^2$-gradient flow of the elastic energy.
For any initial curve lying merely in the energy space we show existence and
parabolic smoothing of the solution. Applying previous results on long time
existence and proving a constrained Lojasiewicz-Simon gradient inequality we
furthermore show convergence to a critical point as time tends to infinity.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess