Blaschke's rolling theorem for manifolds with boundary

For a complete Riemannian manifold M with compact boundary partial derivative M denote by C-partial derivative M the cut locus of partial derivative M in M. The rolling radius of M is Roll(M) := dist(partial derivative M, C-partial derivative M). Let Focal(partial derivative M) be the focal distance of partial derivative M in M. Then conditions are given that imply the equality Roll(M) = Focal(partial derivative M). This generalizes Blaschke's rolling theorem from bounded convex domains in Euclidean space to more general Euclidean domains and to Riemannian manifolds with boundary.