Mitja Nedić: Purisubharmonic and q-convex functions

We begin by recalling some basic notions of complex manifolds and the tangent and cotangent bundle. With the help of the Levi form we then define plurisubharmonic functions and look at the equivalence of this definition with others. Next we look at some properties and examples of plurisubharmonic functions along with the  approximation theorem. We then define the notion of q-convexity in the case of functions, manifolds and bundles and explore some examples and counterexamples. In general we have theorems that connect metric q-convexity of holomorphic bundles with the q-convexity of complex manifolds. Finally we mention at some results in Morse theory that are connected with plurisubharmonic and q-convex functions.