Fixed frequency eigenfunction immersions and supremum norms of random waves

Yaiza  Canzani; Boris  Hanin

doi:10.3934/era.2015.22.76

Article Contents

2015, Volume 22: 76-86. Doi: 10.3934/era.2015.22.76 open access

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Fixed frequency eigenfunction immersions and supremum norms of random waves

Yaiza Canzani^1, and
Boris Hanin^2,

1.
Department of Mathematics, Harvard University, Cambridge
2.
Department of Mathematics, Massachusetts Institute of Technology, Cambridge

Received: December 31, 2014

Revised: May 31, 2015

Published: December 2014

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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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Mathematics Subject Classification: 35P05 (Pri), 53C42 (Sec).

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