Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of nonnegatively curved surfaces relative to a curve   We prove that any properly oriented $C^{2,1}$ isometric immersion of a
positively curved Riemannian surface M into Euclidean 3-space is uniquely
determined, up to a rigid motion, by its values on any curve segment in M. A
generalization of this result to nonnegatively curved surfaces is presented as
well under suitable conditions on their parabolic points. Thus we obtain a
local version of Cohn-Vossen's rigidity theorem for convex surfaces subject to
a Dirichlet condition. The proof employs in part Hormander's unique
continuation principle for elliptic PDEs. Our approach also yields a short
proof of Cohn-Vossen's theorem.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph