EVENT DETAILS AND ABSTRACT

Title: L^p norms of eigenfunctions and Kakeya-Nikodym averages
Speaker: Matt Blair
Speaker Info: University of New Mexico
Brief Description:
Special Note:
Abstract:

We consider the problem of determining upper bounds on the growth of L^p norms of eigenfunctions of the Laplacian on a compact Riemannian manifold. After an introduction to the problem, we will discuss recent work of C. Sogge and the speaker with C. Sogge relating such growth to mass concentration in frequency dependent tubes about geodesic segments. We then show that this yields improved L^p bounds for manifolds with nonpositive sectional curvatures, extending a result of Sogge-Zelditch to higher dimensions.