Singular and tangent slit solutions to the Loewner equation

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We consider the Loewner differential equation generating univalent maps of the unit disk (or of the upper half-plane) onto itself minus a single slit. We prove that the circular slits, tangent to the real axis are generated by Hölder continuous driving terms with exponent 1/3 in the Loewner equation. Singular solutions are described, and the critical value of the norm of driving terms generating quasisymmetric slits in the disk is obtained.
8 pages

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Complex Variables, 30C35, 30C20

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http://salesiana.dossiersoluciones.com/handle/123456789/163295

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.1048
 http://arxiv.org/abs/0708.1048

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arXiv