|Dept.||Johns Hopkins University|
In this talk, we start talking about known results of previous work for eigenfunction restriction estimates on compact Riemannian manifolds without boundary for the Laplace-Beltrami operator, or Laplacian. We then discuss the role of the curvatures of both manifolds and submanifolds, which allows us to obtain better estimates compared to the case of general manifolds or submanifolds. We will also consider the analogues of the Schrodinger operator with singular potentials and consider some related current/future projects. This is joint work with Matthew Blair.