  At low temperatures, phonon scattering can become so weak that phonon
transport becomes ballistic. We calculate the ballistic phonon conductance G
for membranes using elasticity theory, considering the transition from three to
two dimensions. We discuss the temperature and thickness dependence and
especially concentrate on the issue of material parameters. For all membrane
thicknesses, the best conductors have, counter-intuitively, the lowest speed of
sound.
