= Green function of killed planar Brownian motion
{c}
{title2=$G_D(z,w)$}
= Brownian Green function
{c}
{synonym}
The density of expected <Brownian occupation time> before exit from a planar domain. For <planar Brownian motion> with <infinitesimal generator> $\tfrac12\Delta$, it obeys $-\tfrac12\Delta_wG_D(z,w)=\delta_z(w)$ and has singularity $-\pi^{-1}\log|w-z|$. A <conformal bijection> preserves this <Dirichlet Green function>: the squared derivative in the <conformal Brownian clock> cancels the area <Jacobian determinant>.
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