Bilinear Strichartz estimates in two dimensional compact manifolds and cubic nonlinear Schrodinger equations

In this thesis, we establish bilinear Strichartz estimates for Schrodinger operators in 2 dimensional compact manifolds without boundary and with boundary. Then we use estimates on manifold with boundary to prove the local well-posed of cubic nonlinear Schrodinger equation in Hs for every s > ⅔ on it.