Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces

Changxing Miao , Christopher D. Sogge , Yakun Xi , Jianwei Yang

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keywords bilinearestimateskakeya-nikodymauthoraveragesblairburqcompact

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We obtain an improvement of the bilinear estimates of Burq, G\'erard and Tzvetkov in the spirit of the refined Kakeya-Nikodym estimates of Blair and the second author. We do this by using microlocal techniques and a bilinear version of H\"ormander's oscillatory integral theorem.

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Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces

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