Gluing copies of a 3-dimensional polyhedron to obtain a closed nonpositively curved pseudomanifold

Burago, D.; Ferleger, S.; Kleiner, B.; Kononenko, A.

doi:10.1090/S0002-9939-01-05554-X

Gluing copies of a 3-dimensional polyhedron to obtain a closed nonpositively curved pseudomanifold
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by D. Burago, S. Ferleger, B. Kleiner and A. Kononenko PDF

Proc. Amer. Math. Soc. 129 (2001), 1493-1498 Request permission

Abstract:

Let $S$ be a smooth 3-dimensional nonpositively curved Riemannian manifold with corners, whose boundary consists of a finite number of geodesically convex nonpositively curved faces (for example, a Euclidean or hyperbolic polyhedron). We show that it is always possible to glue together finitely many copies of $S$ so as to get a nonpositively curved pseudomanifold without boundary.

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