p-Harmonic functions

Method

Let $(M,g)$ be a Riemannian manifold. This project concerned itself with the study of the $p$-harmonic equation $\tau^p(\phi) = 0,$ where $\phi:M\to\mathbb{C}$ is a complex-valued function, $\tau$ denotes the Laplace-Beltrami operator on $(M,g)$, and $\tau^p$ is its $p$-th iterate. In particular, the main focus of the project was the construction of explicit examples of such function using the so-called method of eigenfunctions.