Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Submanifolds of warped product manifolds $I\times_f S^{m-1}(k)$}} from a
  $p$-harmonic viewpoint   We study $p$-harmonic maps, $p$-harmonic morphisms, biharmonic maps, and
quasiregular mappings into submanifolds of warped product Riemannian manifolds
${I}\times_f S^{m-1}(k)\, $ of an open interval and a complete
simply-connecteded $(m-1)$-dimensional Riemannian manifold of constant
sectional curvature $k$. We establish an existence theorem for $p$-harmonic
maps and give a classification of complete stable minimal surfaces in certain
three dimensional warped product Riemannian manifolds ${\bf R}\times_f
S^{2}(k)\, ,$ building on our previous work. When $f \equiv\, $ Const. and
$k=0$, we recapture a generalized Bernstein Theorem and hence the Classical
Bernstein Theorem in $R^3$. We then extend the classification to parabolic
stable minimal hypersurfaces in higher dimensions.

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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org