Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational proof of Alexandrov's convex cap theorem   We give a variational proof of the existence and uniqueness of a convex cap
with the given upper boundary. The proof uses the concavity of the total scalar
curvature functional on the space of generalized convex caps. As a byproduct,
we prove that generalized convex caps with the fixed boundary are globally
rigid, that is uniquely determined by their curvatures.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas