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arXiv · 2605.01842

A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded

David Kalaj
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Abstract

We construct, for every \(0<k<1\), a bounded globally univalent harmonic mapping \[ f=h+\overline g \colon \D\to\C \] such that \[ |g'(z)|\le k|h'(z)|,\qquad z\in\D, \] 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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David Kalaj. 2026-05-03. A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded. https://arxiv.org/abs/2605.01842

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