Effects of Electron-Electron Scattering in Wide Ballistic Microcontacts

We calculate the corrections to the Sharvin conductance of ballistic multimode microcontacts that result from electron--electron scattering in the leads. Using a semiclassical Boltzmann equation, we obtain that these corrections are {\it positive} and scale with temperature as $T^2\ln(E_F/T)$ for three-dimensional contacts and as $T$ for two-dimensional ones. These results are relevant to recent experiments on 2DEG contacts.