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](http://onlinelibrary.wiley.com/doi/10.1002/1522-2616%28200103%29223:1%3C103%3a%3aAID-MANA103%3E3.0.CO;2-S/abstract;jsessionid=005267834BD1D70906C8A0732ADCAD9B.d02t03?systemMessage=Wiley+Online+Library+will+be+disrupted+4+June+from+10-12+BST+for+monthly+maintenance) 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?



Basic results in bounded geometry
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.


