Non-doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-caratheodory Spaces Presents a study that intends to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Caratheodory space. This title analyzes various concrete applications to the setting of Carnot groups and also presents an application to the solvability of the subelliptic Neumann problem.