arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1408.0882math.CV
收藏

狭缝边的调和测度的渐近比

Asymptotic ratio of harmonic measures of slit sides

Dmitri Prokhorov, Dmitrii Ukrainskii

摘要:

本文讨论了弦Loewner方程的解的几何性质,该方程是基于对上半平面中由驱动项产生的狭缝边的奇异解和调和测度的比较而建立的。对于在给定角度下与直线相切的狭缝和与实轴相切的圆弧高阶相切的狭缝,给出了狭缝边的调和测度的渐近比.

英文摘要:

The article is devoted to the geometry of solutions to the chordal Loewner equation which is based on the comparison of singular solutions and harmonic measures for the sides of a slit in the upper half-plane generated by a driving term. An asymptotic ratio for harmonic measures of slit sides is found for a slit which is tangential to a straight line under a given angle, and for a slit with high order tangency to a circular arc tangential to the real axis.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑