Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: PHH harmonic submersions are stable   We prove that harmonic PHH submersions are (weakly) stable.

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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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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: funct-an
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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: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg