[en] The authors discuss various properties of the ground state of a Bose-condensed dilute gas confined by an external potential. They devote particular attention to the role played by the interaction in determining the kinetic energy of the system and the aspect ratio of the velocity distribution. The structure of the wave function near the classical turning point is discussed and the drawback of the Thomas-Fermi approximation is explicitly pointed out. They consider also states with quantized vorticity and calculate the critical angular velocity for the production of vortices. The presence of vortex states is found to increase the stability of the condensate in the case of attractive interactions