Generalized connected sum construction for constant scalar curvature   metrics
  We consider the problem of constructing solutions to the Yamabe equation (i.e. conformal constant scalar curvature metrics) on the generalized connected sum M = (M_1) #_K (M_2) of two compact Riemannian manifolds (M_1,g_1) and (M_2,g_2) along a common (isometrically embedded) submanifold (K,g_K) of codimension greater or equal than 3. 
Lorenzo Mazzieri