Comments on the Green's function of a planar domain

Diganta Borah, Pranav Haridas, Kaushal Verma

Published 2016-05-14Version 1

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.