Comments on the Green's function of a planar domain
Complex Variables
2016-05-17 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
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 -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.
Keywords
Cite
@article{arxiv.1605.04397,
title = {Comments on the Green's function of a planar domain},
author = {Diganta Borah and Pranav Haridas and Kaushal Verma},
journal= {arXiv preprint arXiv:1605.04397},
year = {2016}
}
Comments
23 pages