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

Filippo Bracci; Ian Graham; Hidetaka Hamada; Gabriela Kohr

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

Complex Variables 2015-01-28 v2 Functional Analysis

Authors: Filippo Bracci , Ian Graham , Hidetaka Hamada , Gabriela Kohr

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.

Keywords

Loewner chains extreme points support points class $S^0$ higher dimensions parametric representation unit ball

Cite

@article{arxiv.1402.5538,
  title  = {Variation of Loewner chains, extreme and support points in the class $S^0$ in higher dimensions},
  author = {Filippo Bracci and Ian Graham and Hidetaka Hamada and Gabriela Kohr},
  journal= {arXiv preprint arXiv:1402.5538},
  year   = {2015}
}

Comments

21 pages, small changes and revised version

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

Abstract

Keywords

Cite

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