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 "geräumig"---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.

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