TITLE: Basic results in bounded geometry
QUESTION [5 upvotes]: I'm doing analysis (dynamical systems) in the context of Riemannian manifolds of bounded geometry and I find myself reproving quite a few standard results/tools from standard differential geometry, such as locally finite covers and subordinate partitions of unity, a tubular neighborhood theorem, smoothing of submanifolds...
The main difference from the standard results is that I require uniformly bounded estimates, so for example the tubular neighborhood must have a uniformly finite size and a uniformly bounded diffeomorphism. This means that I cannot simply generalize the standard proofs.
I'm not familiar with bounded geometry. The only reference with explicit details I found is Schick: Manifolds with Boundary and of Bounded Geometry where a uniformly locally finite cover with subordinate partition of unity is proven.
Are there other books or articles which include similar results in the context of bounded geometry?

REPLY [2 votes]: Many results, in particular about Sobolev spaces, for Riemannian manifolds with bounded geometry, are in:

J. Eichhorn.
Global Analysis on Open Manifolds.
Nova Science Publishers Inc., New York, 2007.
H. Triebel.
Theory of Function Spaces. II, Volume 84 of Monographs
in Mathematics.
Birkhauser Verlag, Basel, 1992.