Sobolev spaces on Riemannian manifolds with bounded geometry: general coordinates and traces (Q2867267)

The authors study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. The spaces are defined by a uniform localization principle. The elements of the function spaces take values in \(\mathbb C\) or in a vector bundle of bounded geometry over the manifold. The main aim is to prove the trace theorem. The traces are taken on submanifolds belonging to a large and naturally defined family. To describe the traces, the authors prove that Fermi coordinates can be used in the uniform localization method instead of the geodesic normal coordinates. More generally, the concept of local trivialization, which fulfils the requirements of uniform localization methods, is introduced.