Eigenfunctions and Nodal Sets

Abstract

This is a survey of recent results on eigenfunctions of the Laplacian on compact Riemannian manifolds and their nodal sets. It is the write-up of my talk at JDG 2011.

60 pages, 5 figures lifted from the web. Comments appreciated

References in corpus (8)

• Lower bounds for nodal sets of eigenfunctions
• Random wave functions and percolation
• Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I
• Concerning the $L^4$ norms of typical eigenfunctions on compact surfaces
• Universality for SLE(4)
• Quantum ergodic restriction theorems, II: manifolds without boundary
• Quantum ergodicity of boundary values of eigenfunctions: A control theory approach
• Critical set of eigenfunctions of the Laplacian

Cited by in corpus (2)

• Fast and Accurate Intrinsic Symmetry Detection
• Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains