Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global minimizers for the doubly-constrained Helfrich energy: the
  axisymmetric case   Since the pioneering work of Canham and Helfrich, variational formulations
involving curvature-dependent functionals, like the classical Willmore
functional, have proven useful for shape analysis of biomembranes. We address
minimizers of the Canham-Helfrich functional defined over closed surfaces
enclosing a fixed volume and having fixed surface area. By restricting
attention to axisymmetric surfaces, we prove the existence of global
minimizers.

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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph