Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weyl problem of isometric immersions revisited   We revisit the classical problem due to Weyl, as well as its generalisations,
concerning the isometric immersions of $\mathbb{S}^2$ into simply-connected
$3$-dimensional Riemannian manifolds with non-negative Gauss curvature. A
sufficient condition is exhibited for the existence of global
$C^{1,1}$-isometric immersions. Our developments are based on the framework
\`{a} la Labourie (Immersions isom\'{e}triques elliptiques et courbes
pseudo-holomorphes, J. Diff. Geom. 30 (1989), 395--424) of studying isometric
immersions using $J$-holomorphic curves. We obtain along the way a
generalisation of a classical theorem due to Heinz and Pogorelov.

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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc