On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable

2014/10/09 by Gal, Sorin G., González-Cervantes, J. Oscar, Sabadini, Irene
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.2623

Abstract

The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of results, among which an Area-type Theorem, Rogosinski inequality, and a Bieberbach-de Branges Theorem for a subclass of slice regular functions. We also discuss some geometric and algebraic interpretations of our results in terms of maps from \mathbb R⁴ to itself. As a tool for subordination we define a suitable notion of composition of slice regular functions which is of independent interest.

Related

• On two Bloch type theorems for quaternionic slice regular functions
• Holomorphicity of slice-regular functions
• Domains of existence of slice regular functions in one quaternionic variable
• Algebra of slice regular functions on non-symmetric domains in several quaternionic variables
• On some quaternionic generalized slice regular functions