Abstract
AbstractLet (ϕt)t≥ 0 be a semigroup of holomorphic functions in the unit disk $\mathbb {D}$
D
and K a compact subset of $\mathbb {D}$
D
. We investigate the conditions under which the backward orbit of K under the semigroup exists. Subsequently, the geometric characteristics, as well as, potential theoretic quantities for the backward orbit of K are examined. More specifically, results are obtained concerning the asymptotic behavior of its hyperbolic area and diameter, the harmonic measure and the capacity of the condenser that K forms with the unit disk.
Funder
Alexander von Humboldt-Stiftung
Julius-Maximilians-Universität Würzburg
Publisher
Springer Science and Business Media LLC
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