Variation of Loewner Chains, Extreme and Support Points in the Class S0S^0 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.Comment: 21 pages, small changes and revised versio