Nonlinear Subelliptic Equations on Carnot Groups

The main objective of this course is to present an extension of Jensen's uniqueness theorem for viscosity solutions of second order uniformly elliptic equations to Carnot groups.  This is done via an extension of the comparison 
principle for semicontinuous functions of Crandall-Ishii-Lions. We first present the details for the Heisenberg group, where the ideas and the calculations are easier to appreciate. We then consider the general case of Carnot groups and present applications to the theory of convex functions and to minimal Lipschitz extensions.