ON TANGENTIAL SLIT SOLUTION OF THE LOEWNER EQUATION
ON TANGENTIAL SLIT SOLUTION OF THE LOEWNER EQUATION
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DOI：
10.5186/aasfm.2016.4142
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
K. Lau;Haihua Wu
中科院分区：
文献类型：
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作者：
K. Lau;Haihua Wu
对于非切向狭缝（t），Loewner方程中驱动函数ε（t）在零附近的行为很好理解;对于切向狭缝，情况不太清楚。本文研究切向缝p，p > 0，其中是在0处相切的圆弧，p在零附近有p+1 p阶.我们的主要结果是给出了ε（t）及其保持器指数在0附近关于p的精确表达式，它与已知结果有着自然的联系.我们还将其推广到一般类型的切向缝，并给出了0附近的增长的估计。
For a non-tangential slit (t), the behavior of the driving function �(t) near zero in the Loewner equation is well understood; for tangential slit, the situation is less clear. In this paper, we investigate the tangential slit p , p > 0, where is a circular arc tangent at 0; p has order p+1 p near zero. Our main result is to give the exact expression of �(t), and its Holder exponent near 0 in terms of p, which has a natural connection with the known results. We also extend this to a general type of tangential slits, and give an estimation of the growth of �(t) near 0.