On Bloch's Theorem for Heat Maps

TL;DR

This paper proves a Bloch-type theorem for heat maps using the contraction mapping principle, focusing on solutions to heat operator equations, extending classical complex analysis results to heat map contexts.

Contribution

It introduces a novel Bloch-type theorem for Bochner-Takahashi $K$-mappings related to heat operators, providing a new analytical tool for heat map analysis.

Findings

Established a Bloch-type theorem for heat maps

Applied contraction mapping principle to heat operator solutions

Extended classical Bloch theorem to heat map context

Abstract

In this paper we give a proof via the contraction mapping principle of a Bloch-type theorem for normalised Bochner-Takahashi $K$-mappings, which are solutions to equations of the form $Lu=0$, where $L$ is the heat operator.