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Analysis and PDE Seminar

Date:
-
Location:
745 Patterson Office Tower
Speaker(s) / Presenter(s):
Matthew Blair, University of New Mexico

Title:  Lp norms of eigenfunctions and Kakeya-Nikodym averages

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 works 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.