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arXiv · 1303.5216

Boundary regular fixed points in Loewner theory

Filippo Bracci·Manuel D. Contreras·Santiago Diaz-Madrigal·Pavel Gumenyuk
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Abstract

We characterize regular fixed points of evolution families in terms of analytical properties of the associated Herglotz vector fields and geometrical properties of the associated Loewner chains. We present several examples showing the rôle of the given conditions. Moreover, we study the relations between evolution families and Herglotz vector fields at regular contact points and prove an embedding result for univalent self-maps of the unit disc with a given boundary regular fixed point into an evolution family with prescribed boundary data.

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Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal, Pavel Gumenyuk. 2013-03-21. Boundary regular fixed points in Loewner theory. https://arxiv.org/abs/1303.5216

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