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Re: Embedding Flat-Surfaces-with-Cone-Points in 3-Space
Posted:
Jul 1, 1996 7:13 PM
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In article <Dtuyy3.GzE@hermes.hrz.uni-bielefeld.de> delgado@Mathematik.Uni-Bielefeld.DE (Olaf Delgado) writes:
In article <RIVIN.96Jun29172719@poincare.ihp.jussieu.fr>,
Igor Rivin <rivin@poincare.ihp.jussieu.fr> wrote:
>It is a theorem of Aleksandrov that every flat surface with positively
>curved (cone angle < 2pi) cone points embeds isometrically as a convex
>polyhedron, and such an embedding is unique.
Could you please give a reference for this theorem?
The canonical reference is A.D. Aleksandrov's book "Convex Polyhedra"
(there exists a german translation if you don't read russian...),
which is highly recommended as a comprehensive introduction to the
field. An easier reference is an article by J.J. Stoker in
Communications in Pure and Applied Mathematics, 1968 (the title is
something like "the geometry of convex polyhedra in the large").
Igor
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