Manifolds of Bounded Geometry
Jaap Eldering · Atlantis Press eBooks · 2013
This chapter treats Riemannian manifolds of bounded geometry. We use bounded geometry to extend uniformity assumptions that were implicit in the compact case to a noncompact setting. We redevelop various technical tools in the context of bounded geometry on Riemannian manifolds, such as a tubular neighborhood and smooth approximation of a submanifold embedding. We also explicitly work out the relation between curvature and holonomy for later use. Finally we use these tools to show how to reduce the main persistence theorem to a setting in a trivial bundle.