  In a recent paper, Ng, Tang and Tsai (Math. Ann. 2020) have found an explicit
formula for the squeezing function of an annulus via the Loewner differential
equation. Their result has led them to conjecture a corresponding formula for
planar domains of any finite connectivity stating that the extremum in the
squeezing function problem is achieved for a suitably chosen conformal mapping
onto a circularly slit disk. In this paper we disprove this conjecture. We also
give a conceptually simple potential-theoretic proof of the explicit formula
for the squeezing function of an annulus which has the added advantage of
identifying all extremal functions.
