关于平面域格林函数的注记
Comments on the Green's function of a planar domain
摘要：
本文研究了复平面上多连通区域的格林函数的几个物理量。其中有一些内在的性质，如测地线，曲率和$L^2$ -上同调的容量度量和临界点的格林函数。所使用的主要思想是仿射缩放的域，该域描述格林函数和相关对象的定量边界行为。
英文摘要：
We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and critical points of the Green's function. The principal idea used is an affine scaling of the domain that furnishes quantitative boundary behaviour of the Green's function and related objects.
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。
