| The aim of this thesis is to present results in nonlinear potential theory mainly on infinite graphs with or without boundary. These objects are similar in many ways to Riemannian manifolds. To this end, we introduce a fundamental notion of p-capacity which allows us to classify finite graphs without boundary as p-parabolic and finite/infinite graphs with boundary as p-hyperbolic, to extend the divergence theorem and its consequences to p-Dirichlet spaces, to prove important analogues to the smooth case such as the Kelvin-Nevanlinna-Royden criterion for p-hyperbolicity, and the criteria of existence/non-existence of solutions to the p-Poisson Equation on p-hyperbolic and p-parabolic graphs. |
