Some properties of large- N two-dimensional Yang-Mills theory

large- N two-dimensional QCD on a cylinder and on a vertex manifold (a sphere with three holes) is investigated. The relation between the saddle-point description and the collective field theory of QCD ₂ is established. Using this relation, it is shown that the Douglas-Kazakov phase transition on a cylinder is associated with the presence of a gap in the eigenvalue distributions for Wilson loops. An exact formula for the phase transition on a disc with an arbitrary boundary holonomy is found. The role of instantons in inducing such transitions is discussed. The zero-area limit of the partition function on a vertex manifold is studied. It is found that this partition function vanishes unless the boundary conditions satisfy a certain selection rule which is an analogue of momentum conservation in field theory.