Restriction of Schrödinger eigenfunctions to submanifolds

2024/08/04 by Xiaoqi Huang, Xing Wang, Huang, Xiaoqi +3
Mathematics · #advanced mathematical theories #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2408.01947

Abstract

For Schrödinger operators H_V=-Δ_g+V with critically singular potentials V on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds. Our method refines the perturbative argument by Blair-Sire-Sogge and enables us to deal with submanifolds of all codimensions. As applications, we obtain improved estimates on negatively curved manifolds and flat tori. In particular, we extend the uniform L² restriction estimates on flat tori by Bourgain-Rudnick to singular potentials.

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