Dalhousie-AARMS AAMP Seminar: Chamsol Park (Johns Hopkins University)

Title: Eigenfunction restriction estimates on curves with nonvanishing geodesic curvatures

Abstract: Studying eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds (without boundary) is one of the interesting topics in Harmonic Analysis. One way to study them is to consider the L^p estimates of the eigenfunctions restricted to submanifolds. In this talk, we briefly summarize previous results and would like to talk about the logarithmic improved analogue for the restriction to curves with nonvanishing geodesic curvatures, in the presence of nonpositive sectional curvatures in the manifolds. If time permits, we will discuss some applications and open problems for the Schrodinger counterparts.