  We show that it is Unique Games-hard to approximate the maximum of a
submodular function to within a factor 0.695, and that it is Unique Games-hard
to approximate the maximum of a symmetric submodular function to within a
factor 0.739. These results slightly improve previous results by Feige,
Mirrokni and Vondr\'ak (FOCS 2007) who showed that these problems are NP-hard
to approximate to within $3/4 + \epsilon \approx 0.750$ and $5/6 + \epsilon
\approx 0.833$, respectively.
