  The effect of phonon scattering by surface roughness on the thermal
conductance in mesoscopic systems at low temperatures is calculated using full
elasticity theory. The low frequency behavior of the scattering shows novel
power law dependences arising from the unusual properties of the elastic modes.
This leads to new predictions for the low temperature depression of the thermal
conductance below the ideal universal value. Comparison with the data of Schwab
et al. [Nature 404, 974 (2000)] suggests that surface roughness on a scale of
the width of the thermal pathway is important in the experiment.
