Loewner chains with complex leading coefficient
Ikkei Hotta
TL;DR
This paper extends classical Loewner chain theorems to cases with complex leading coefficients, providing new criteria for univalence and quasiconformal extensions without normalization.
Contribution
It generalizes key Loewner chain theorems to complex coefficients and introduces novel univalence and extension criteria.
Findings
Classical theorems hold without normalization for complex coefficients
New univalence criteria established
Quasiconformal extension conditions derived
Abstract
In this paper we confirm that several crucial theorems due to Pommerenke and Becker for the theory of Loewner chains work well without normalization on the complex-valued first coefficient. As applications of those considerations, some new univalent and quasiconformal extension criteria are given in the last section.
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Taxonomy
TopicsAnalytic and geometric function theory · Pharmacological Effects of Medicinal Plants · Nonlinear Partial Differential Equations