Variation of Loewner chains, extreme and support points in the class $S^0$ in higher dimensions

TL;DR

This paper introduces a new family of Loewner chains in higher-dimensional unit balls, enabling the construction and analysis of support points, extreme points, and reachable functions within the class $S^0$, advancing the understanding of parametric representations.

Contribution

It presents a novel 'geräumig' family of Loewner chains in higher dimensions, facilitating the study of support and extreme points in the class $S^0$ of parametric mappings.

Findings

Constructed a new family of Loewner chains in higher dimensions.

Analyzed support points and extreme points in the class $S^0$.

Provided methods to generate functions reachable at specific times.

Abstract

We introduce a family of natural normalized Loewner chains in the unit ball, which we call "ger\"aumig"---spacious---which allow to construct, by means of suitable variations, other normalized Loewner chains which coincide with the given ones from a certain time on. We apply our construction to the study of support points, extreme points and time-$\log M$-reachable functions in the class $S^0$ of mappings admitting parametric representation.