Problems related to the concentration of eigenfunctions

Sogge, Christopher D.

Journées équations aux dérivées partielles (2015), article no. 9, 11 p.

We survey recent results related to the concentration of eigenfunctions. We also prove some new results concerning ball-concentration, as well as showing that eigenfunctions saturating lower bounds for $L^1$-norms must also, in a measure theoretical sense, have extreme concentration near a geodesic.

Classification : 58J51, 35A99, 42B37
Mots clés : Eigenfunctions, Kakeya-Nikodym averages

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