Reshetnyak gluing theorem
In metric geometry, the Reshetnyak gluing theorem gives information on the structure of a geometric object build by using as building blocks other geometric objects, belonging to a well defined class. Intuitively, it states that a manifold obtained by joining 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.Statement
Theorem: Let be complete locally compact geodesic metric spaces of CAT curvature, and convex subsets which are isometric. Then the manifold, obtained by gluing all along all, is also of CAT curvature.
For an exposition and a proof of the Reshetnyak Gluing Theorem, see.
