Collisions and spirals of Loewner traces
We analyze Loewner traces driven by functions asymptotic to κ 1 − t . We prove a stability result when κ ≠ 4 , and we show that κ = 4 can lead to nonlocally connected hulls. As a consequence, we obtain a driving term λ ( t ) so that the hulls driven by κ λ ( t ) are generated by a continuous curve f...
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| Veröffentlicht in: | Duke mathematical journal 2010-09, Vol.154 (3), p.527-573 |
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| container_title | Duke mathematical journal |
| container_volume | 154 |
| creator | Lind, Joan Marshall, Donald E. Rohde, Steffen |
| description | We analyze Loewner traces driven by functions asymptotic to κ 1 − t . We prove a stability result when κ ≠ 4 , and we show that κ = 4 can lead to nonlocally connected hulls. As a consequence, we obtain a driving term λ ( t ) so that the hulls driven by κ λ ( t ) are generated by a continuous curve for all κ > 0 with κ ≠ 4 , but not when κ = 4 , so that the space of driving terms with continuous traces is not convex. As a byproduct, we obtain an explicit construction of the traces driven by κ 1 − t and a conceptual proof of the corresponding results of Kager, Nienhuis, and Kadanoff. |
| doi_str_mv | 10.1215/00127094-2010-045 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0012-7094 |
| ispartof | Duke mathematical journal, 2010-09, Vol.154 (3), p.527-573 |
| issn | 0012-7094 1547-7398 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1283865312 |
| source | Project Euclid Complete |
| subjects | 30C20 30C30 30C45 30C62 bounded rotation Conformal mappings of special domains convex etc. Numerical methods in conformal mapping theory [See also 65E05] Quasiconformal mappings in the plane Special classes of univalent and multivalent functions (starlike |
| title | Collisions and spirals of Loewner traces |
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