Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions
classification
🧮 math.AP
math.CAmath.DG
keywords
eigenfunctionsestimateskakeya-nikodymmicrolocalobtainadaptedboundsdecomposition
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We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving a natural decomposition of phase space that is adapted to the geodesic flow.
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