Solution of a Loewner Chain Equation in Several Complex Variables
Mircea Voda
TL;DR
This paper provides a solution to the Loewner chain equation in several complex variables under specific conditions on the infinitesimal generator, and explores related classes of complex mappings.
Contribution
It introduces a solution to the Loewner chain equation for a class of infinitesimal generators and studies associated complex mapping classes.
Findings
Solution to the Loewner chain equation for generators with m(A)>0
Analysis of spirallike and asymptotically spirallike mappings
Characterization of mappings with parametric representation
Abstract
We find a solution to the Loewner chain equation in the case when the infinitesimal generator satisfies h(0,t)=0, Dh(0,t)=A for any linear operator with m(A)>0. We also study the related classes of spirallike mappings, mappings with parametric representation and asymptotically spirallike mappings.
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