Growth theorems for slice Dirac-regular mappings over Clifford algebras

TL;DR

This paper introduces a new class of slice Dirac-regular mappings over Clifford algebras, proves their properties related to the Dirac operator, and establishes growth theorems for specific types of these mappings.

Contribution

It defines slice Dirac-regular mappings based on O(3)-stem mappings and proves growth theorems for starlike and symmetric cases in Clifford algebras.

Findings

Slice mappings vanish under the slice Dirac operator.

Generalized Cauchy-Riemann equations are satisfied by O(3)-stem mappings.

Growth theorems are established for starlike and symmetric mappings.

Abstract

In this paper, we define a class of slice Dirac-regular mappings of several variables over Clifford algebras, based on the concept of O(3)-stem mappings. We prove that the slice mappings vanish under the slice Dirac operator, which is equivalent to its O(3)-stem mappings satisfy the generalized version of the Cauchy-Riemann equation. Moreover, we establish the growth theorem for slice Dirac-regular starlike mappings in the slice cones of Clifford algebras, as well as for slice Dirac-regular k-fold symmetric mappings.