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arXiv · 2408.01947

Restriction of Schrödinger eigenfunctions to submanifolds

Xiaoqi Huang·Xing Wang·Cheng Zhang
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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 $L^2$ restriction estimates on flat tori by Bourgain-Rudnick to singular potentials.

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Xiaoqi Huang, Xing Wang, Cheng Zhang. 2025-09-22. Restriction of Schrödinger eigenfunctions to submanifolds. https://arxiv.org/abs/2408.01947

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