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 of 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.