Local and global analysis of eigenfunctions

Details Local and global analysis of eigenfunctions Local and global analysis of eigenfunctions

2009-03-19

arxiv.org/abs/0903.3420v1

Advanced Lectures in Mathematics (ALM) 7, 545-658 (2008)

Mathematics

Analysis of PDEs

A survey on eigenfunctions for the Handbook of Geometric Analysis, no. 1: L. Ji, P. Li, R. Schoen and L. Simon (eds.),

Scientific paper

This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds
(mainly compact and without boundary). We discuss both local results obtained
by analyzing eigenfunctions on small balls, and global results obtained by wave
equation methods. Among the main topics are nodal sets, quantum limits, and
$L^p$ norms of global eigenfunctions.

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