  We provide asymptotically sharp bounds for the Gaussian surface area and the
Gaussian noise sensitivity of polynomial threshold functions. In particular we
show that if $f$ is a degree-$d$ polynomial threshold function, then its
Gaussian sensitivity at noise rate $\epsilon$ is less than some quantity
asymptotic to $\frac{d\sqrt{2\epsilon}}{\pi}$ and the Gaussian surface area is
at most $\frac{d}{\sqrt{2\pi}}$. Furthermore these bounds are asymptotically
tight as $\epsilon\to 0$ and $f$ the threshold function of a product of $d$
distinct homogeneous linear functions.
