Lq Estimates on the Restriction of Schr\"odinger Eigenfunctions with singular potentials

We consider eigenfunction estimates in Lᵖ for Schr\"odinger operators, HV=-Δg+V(x), on compact Riemannian manifolds $(M, g)$. Eigenfunction estimates over the full manifolds were already obtained by Sogge {Sogge1988concerning} for V≡ 0 and the first author, Sire, and Sogge {BlairSireSogge2021Quasimode}, and the first author, Huang, Sire, and Sogge {BlairHuangSireSogge2022UniformSobolev} for critically singular potentials V. For the corresponding restriction estimates for submanifolds, the case V≡ 0 was considered in Burq, G\'erard, and Tzvetkov {BurqGerardTzvetkov2007restrictions}, and Hu {Hu2009lp}. In this article, we will handle eigenfunction restriction estimates for some submanifolds Σ on compact Riemannian manifolds $(M, g)$ with n:= M≥ 2, where V is a singular potential.