Rough isometries and the parabolicity of riemannian manifolds
Rough isometries and the parabolicity of riemannian manifolds
When we study non-compact complete riemannian manifolds, we observe that quasi-isometric deformations of their metrics do not alter global or qualita- tive properties of the manifolds: For example, two complete riemannian mani- folds quasi-isometric to each other obviously have the same volume growth rate.On the other hand, for a non-compact …