Defect measures of eigenfunctions with maximal $ L^\infty $ growth

Jeffrey Galkowski

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arXiv · 1704.01452

Defect measures of eigenfunctions with maximal $ L^\infty $ growth

Jeffrey Galkowski

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Abstract

We study the relationship between $L^\infty$ growth of eigenfunctions and their $L^2$ concentration as measured by defect measures. In particular, we characterize the defect measures of any sequence of eigenfunctions with maximal $L^\infty$ growth, showing that they must be neither more concentrated nor more diffuse than the zonal harmonics. As a consequence, we obtain new proofs of results on the geometry manifolds with maximal eigenfunction growth obtained by Sogge--Zelditch, and Sogge--Toth--Zelditch.

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Jeffrey Galkowski. 2017-04-05. Defect measures of eigenfunctions with maximal $ L^\infty $ growth. https://arxiv.org/abs/1704.01452

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