Program
Mathematics
College
Arts and Sciences
Student Level
Doctoral
Location
Student Union Building, Ballroom C
Start Date
8-11-2021 11:00 AM
End Date
8-11-2021 1:00 PM
Abstract
There have been ways to study the eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds (without boundary), one of which is to consider the L^p estimates of the eigenfunctions restricted to submanifolds in the given manifolds. Burq, Gérard, and Tzvetkov, and Hu studied many types of these restricted estimates, and one of them was the L^2 restriction estimates on curves with nonvanishing geodesic curvatures. In this talk, we would like to talk about their logarithmic improved analogues, in the presence of nonpositive sectional curvatures in the given compact Riemannian manifolds.
Eigenfunction Restriction Estimates on curves with nonvanishing geodesic curvatures
Student Union Building, Ballroom C
There have been ways to study the eigenfunctions of the Laplace-Beltrami operator on compact Riemannian manifolds (without boundary), one of which is to consider the L^p estimates of the eigenfunctions restricted to submanifolds in the given manifolds. Burq, Gérard, and Tzvetkov, and Hu studied many types of these restricted estimates, and one of them was the L^2 restriction estimates on curves with nonvanishing geodesic curvatures. In this talk, we would like to talk about their logarithmic improved analogues, in the presence of nonpositive sectional curvatures in the given compact Riemannian manifolds.
