A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded
Abstract
We construct, for every \(0<k<1\), a bounded globally univalent harmonic mapping \[ f=h+ g \] such that \[ |g'(z)| k|h'(z)|, z∈, \] while the analytic part \(h\) is unbounded. The construction is based on a bounded logarithmic spiral map on a far right horizontal strip, together with a smaller logarithmic perturbation.
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