Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularities of flat extensions from generic surfaces with boundaries   We solve the problem on flat extensions of a generic surface with boundary in
Euclidean 3-space, relating it to the singularity theory of the envelope
generated by the boundary. We give related results on Legendre surfaces with
boundaries via projective duality and observe the duality on boundary
singularities. Moreover we give formulae related to remote singularities of the
boundary-envelope.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin