The Harnack distance and estimates of subharmonic functions from below on the unit disc

Abstract

General estimates from below of holomorphic and subharmonic functions play one of the key roles in the theory of growth of holomorphic and subharmonic functions and in general in the theory of potential. At the same time, the most diverse technical apparatus was often used for this. In one of our recent papers, we showed in fairly general cases that in fact such a wide set of tools is not required. The classic Harnack distance is almost always enough. In this article, we will illustrate how this works in the cases of the unit disc in the complex plane.