Height estimate and Lipschitz-graph approximation of length minimizers

In this thesis we deal with length minimizing curves in sub-Riemannian manifolds, particularly in a special type of Carnot groups. We will show two results: the first one, called the Height Estimate, gives an upper bound for a quantity of the curve in terms of its excess, and will be used in order to obtain the second result, which is an approximation of such length minimizers by means of a Lipschitz-graph.