A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911642947682304 |
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| author | Kalaj, David |
| author_facet | Kalaj, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01842 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded Kalaj, David Complex Variables 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. |
| title | A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2605.01842 |