  We study, within the Schwinger-boson approach, the ground-state structure of
two Heisenberg antiferromagnets on the triangular lattice: the J1-J2 model,
which includes a next-nearest-neighbor coupling J2, and the
spatially-anisotropic J1-J'1 model, in which the nearest-neighbor coupling
takes a different value J'1 along one of the bond directions. The motivations
for the study of these systems range from general theoretical questions
concerning frustrated quantum spin models to the concrete description of the
insulating phase of some layered molecular crystals. For both models, the
inclusion of one-loop corrections to saddle-point results leads to the
prediction of nonmagnetic phases for particular values of the parameters J1/J2
and J'1/J1. In the case of the J1-J2 model we shed light on the existence of
such disordered quantum state, a question which is controversial in the
literature. For the J1-J'1 model our results for the ground-state energy,
quantum renormalization of the pitch in the spiral phase, and the location of
the nonmagnetic phases, nicely agree with series expansions predictions.
