High Frequency Eigenfunction Immersions and Supremum Norms of Random Waves

Yaiza Canzani; Boris Hanin

doi:10.3934/era.2015.22.76

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arXiv · 1406.2309

High Frequency Eigenfunction Immersions and Supremum Norms of Random Waves

Yaiza Canzani·Boris Hanin

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Abstract

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.

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BibTeX RIS

Yaiza Canzani, Boris Hanin. 2014-06-07. High Frequency Eigenfunction Immersions and Supremum Norms of Random Waves. https://doi.org/10.3934/era.2015.22.76

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