Variation of Loewner chains, extreme and support points in the class   $S^0$ in higher dimensions
  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. 
Filippo Bracci, Ian Graham, Hidetaka Hamada, Gabriela Kohr
math.CV math.FA