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Fixed frequency eigenfunction immersions and supremum norms of random waves

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  • A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and others on upper bounds for the sup-norms of random linear combinations of high frequency eigenfunctions.
    Mathematics Subject Classification: 35P05 (Pri), 53C42 (Sec).


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