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Caltech

Caltech/UCLA Joint Analysis Seminar

Friday, October 7, 2016
4:00pm to 5:00pm
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L^p norms of eigenfunctions and Kakeya-Nikodym averages
Matthew Blair, Associate Professor , Department of Mathematics & Statistics, University of New Mexico,

We consider the problem of determining optimal upper bounds on the growth of L^p norms of eigenfunctions of the Laplacian on a compact Riemannian manifold in the high frequency limit. After an introduction to the problem, we will discuss results relating such upper bounds to mass concentration estimates in tubes about geodesic segments with a frequency dependent diameter. When the manifold has nonpositive sectional curvatures, it can be shown that there is a logarithmic gain in the trivial mass concentration estimates over these tubes, translating to improvements in the L^p bounds. These are results in joint works with C. Sogge.

For more information, please phone 626-395-4335 or email [email protected].