We answer a question raised by Ahmet Sebbar and Thérèse Falliero (2007) by showing that for every finitely connected planar domain
Ω
\Omega
there exists a compact subset
K
⊂
Ω
K\subset \Omega
, independent of
w
w
, containing all critical points of Green’s function
G
(
z
,
w
)
G(z,w)
of
Ω
\Omega
with pole at
w
∈
Ω
w\in \Omega
.