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 rle 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.
Bracci, F., Contreras, M.d., Diaz-Madrigal, S., Gumenyuk, P. (2015). Boundary regular fixed points in Loewner theory. ANNALI DI MATEMATICA PURA ED APPLICATA, 194(1), 221-245 [10.1007/s10231-013-0372-4].
Boundary regular fixed points in Loewner theory
Bracci F.;
2015-01-01
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 rle 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
