Potential Theory and Carnot
Groups
Contents
1. Abstract potential theory.
Harmonic spaces,
sub-harmonic functions, harmonic measures, Perron-Wiener method.
2. Carnot groups.
A self-contained
introduction. Sub-Laplacians and fundamental solutions. Riesz representation
theorem of
sub-harmonic
functions. Thinness at infinity and Phragmen-Lindelof principle. Applications:
Hanack-Liouville
Theorems. Symmetry
properties of solutions to semilinear equations.