區域的映照半徑與格林函數

<正> §1.設a_1,a_2是z平面上兩個不同的有限點,G_1和G_2是z平面上不相重疊的兩個單連區域,a_i∈G_i,i=1,2.記R(a_i,G_i)是區域G_i關於a_i真的映照半徑.記

ON THE MAPPING RADII AND GREEN FUNCTIONS OF NON-OVERLAPPING DOMAINS

Let G_1, G_2 be two non-overlapping domains contained in certain domain G. Let R(a_i, G_i) be the mapping radius of domain G_i with respect to a_i (a_i ∈ G_i), i.e. the reciprocal of capacity constant of G_i with respect to a_i. Let g(z, ζ) be the Green function of G with a logarithmic pole at ζ, and h(z, ζ) be the regular part of g(z, ζ), i.e. In the present note, we prove that, for x_1>0, x_2 > 0, by the method of extremal length.