L q estimates on the restriction of Schrödinger eigenfunctions with singular potentials

We consider eigenfunction estimates in Lq for Schrödinger operators, HV=−Δg+V(x), on compact Riemannian manifolds (M, g). Eigenfunction estimates over the full manifolds were already obtained by Sogge for V≡0, and by the first author, Sire, and Sogge and the first author, Huang, Sire, and Sogge for critically singular potentials V. For the corresponding restriction estimates for submanifolds, the case V≡0 was considered in Burq, Gérard, and Tzvetkov, and in Hu. In this article, we will handle eigenfunction restriction estimates for some submanifolds Σ on compact Riemannian manifolds (M, g) with n:=dim⁡M≥2, where V is a singular potential.