Problems related to the concentration of eigenfunctions

2015/10/26 by Sogge, Christopher D. · 1 citation
#42B37 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 58J51 #Secondary 35A99

paper · doi:10.48550/arxiv.1510.07723

Abstract

We survey recent results related to the concentration of eigenfunctions. We also prove some new results concerning ball-concentration, as well as showing that eigenfunctions saturating lower bounds for L¹-norms must also, in a measure theoretical sense, have extreme concentration near a geodesic.

Cited by

• L^p-Logvinenko-Sereda sets and L^p-Carleson measures on compact manifolds

Related

• Eigenfunction concentration via geodesic beams
• Concentration of eigenfunctions near a concave boundary
• Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
• L^p concentration estimates for the Laplacian eigenfunctions near submanifolds
• Concentration of symmetric eigenfunctions