Concentration of eigenfunctions on singular Riemannian manifolds

2024/10/27 by Dietze, Charlotte, Read, Larry · 1 citation
#35P20 #Analysis of PDEs (math.AP) #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 58C40 #Secondary: 53C17 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2410.20563

Abstract

We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator plus a singular potential. In a supercritical parameter regime, we identify the rate of concentration and profile of the high-frequency eigenfunctions that accumulate at the boundary. We give an application to acoustic modes on gas planets.

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• The critical case for the concentration of eigenfunctions on singular Riemannian manifolds

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