  We prove that the Gaussian broadcast channel with two destinations admits the
strong converse property. This implies that for every sequence of block codes
operated at a common rate pair with an asymptotic average error probability
$<1$, the rate pair must lie within the capacity region derived by Cover and
Bergmans. The main mathematical tool required for our analysis is a logarithmic
Sobolev inequality known as the Gaussian Poincar\'e inequality.
