Uniformly Regular and Singular Riemannian Manifolds

A detailed study of uniformly regular Riemannian manifolds and manifolds with singular ends is carried out in this paper. Such classes of manifolds are of fundamental importance for a Sobolev space solution theory for parabolic evolution equations on non-compact Riemannian manifolds with and without boundary. Besides pointing out this connection in some detail we present large families of uniformly regular and singular manifolds which are admissible for this analysis.