Abstract
Let be a smooth, compact Riemannian manifold, and let be an -normalized sequence of Laplace eigenfunctions, . Given a smooth submanifold of codimension , we find conditions on the pair for which One such condition is that the set of conormal directions to that are recurrent has measure . In particular, we show that the upper bound holds for any if is a surface with Anosov geodesic flow or a manifold of constant negative curvature. The results are obtained by characterizing the behavior of the defect measures of eigenfunctions with maximal averages.
Citation
Yaiza Canzani. Jeffrey Galkowski. "On the growth of eigenfunction averages: Microlocalization and geometry." Duke Math. J. 168 (16) 2991 - 3055, 1 November 2019. https://doi.org/10.1215/00127094-2019-0020
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