Global theorems represent the highlights of classical Differential Geometry.
Prominent examples
are Fenchel`s, Milnor`s, Schwarz`s, Schur`s theorems and Blaschke`s rolling
theorem. They build the scope of this work, in which we give sufficient
conditions for the uniqueness of the foot point and nearest point from given
coordinates to a regular $C^2$ curve in $/mathbf{R}^n$. This is a
criterion for the free rolling of balls on open space curves, which
generalises Blaschke`s rolling theorem to higher dimensions. Finally the results
are applied to hypersurfaces.
Our main results are the theorems
/ref{Satz:3d2proj} and /ref{Satz:freiesRollen} for curves and theorems
/ref{Satz:LotFlae} and /ref{Satz:Roll:Flae} for surfaces.