  The Blaschke rolling disk theorem is a classical inclusion principle in
differential geometry. This states that a planar convex domain whose boundary
is a curve of class $C^2$ with (signed) curvature not exceeding a positive
constant $\kappa$ is such that for each point on its boundary there exists a
disk of radius ${1}/{\kappa}$ tangent to the boundary included in the closure
of the domain.
  We describe geometric conditions relying exclusively on curvature and
independent of any kind of convexity that allows us to give necessary and
sufficient conditions for the existence of rolling disks for planar domains
that are not necessarily convex. We finish by presenting an algorithm leading
to a decomposition of any planar domain into a finite number of maximal rolling
regions.

Differential Geometry;Metric Geometry