Ecological Barriers and Convergence: a Note on Geometry in Spatial Growth Models

We introduce an AK spatial growth model with a general geographical structure. The dynamics of the economy is described by a partial differential equation on a Riemannian manifold. The morphology interacts with the spatial dynamics of the capital and is one determinant of the qualitative behavior of the economy. We characterize on the geographical structure the conditions that guarantee, in the long run, the convergence of the detrended capital across locations and those inducing spatial capital agglomeration