In metric geometry, the Reshetnyak gluing theorem gives information on the structure of a geometric object built by using as building blocks other geometric objects, belonging to a well defined class.
Intuitively, it states that a manifold obtained by joining (i.e. "gluing") together, in a precisely defined way, other manifolds having a given property inherit that very same property.
The theorem was first stated and proved by Yurii Reshetnyak in 1968.
be complete locally compact geodesic metric spaces of CAT curvature
For an exposition and a proof of the Reshetnyak Gluing Theorem, see (Burago, Burago & Ivanov 2001, Theorem 9.1.21).
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