Bloch’s theorem for heat mappings

Abstract

In this paper we give a proof via the contraction mapping principle of a Bloch-type theorem for (normalised) heat Bochner-Takahashi K-mappings, that is, mappings that are solutions to the heat equation, and which also satisfy a weak form of K-quasiregularity. We also provide estimates from below for the radius of the univalent balls covered by this family of functions.