Singular and tangent slit solutions to the Lowner equation
Singular and tangent slit solutions to the Lowner equation
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DOI：
10.1007/978-3-7643-9906-1_23
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发表时间：
2007-08
期刊：
影响因子：
--
通讯作者：
D. Prokhorov;A. Vasil’ev
中科院分区：
文献类型：
--
作者：
D. Prokhorov;A. Vasil’ev
我们考虑Löwner微分方程生成单位圆盘（或上半平面）到自身减去一个单缝的单叶映射。证明了与真实的轴相切的圆缝是由Löwner方程中指数为1/3的Hölder连续驱动项产生的。描述了奇异解，得到了圆盘中产生拟对称狭缝的驱动项范数的临界值。
We consider the Löwner 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 Löwner equation. Singular solutions are described, and the critical value of the norm of driving terms generating quasisymmetric slits in the disk is obtained.