Radial Variation of Positive Harmonic Functions and Bloch Functions

In this thesis two topics are treated. First, we provide variational estimates for Bloch functions on the unit ball of R d extending previous work on the Anderson conjecture for conformal maps on the unit disc. The second part presents the necessary modifications of the proof by Mozolyako and Havin on the variation of positive harmonic functions to work for Lipschitz domains instead of C 2 domains.