  We investigate how to glue hyperconvex (or injective) metric spaces such that
the resulting space remains hyperconvex. We give two new criteria, saying that
on the one hand gluing along strongly convex subsets and on the other hand
gluing along externally hyperconvex subsets leads to hyperconvex spaces.
Furthermore, we show by an example that these two cases where gluing works are
opposed and cannot be combined.
