This paper is concerned with Schrödinger equations with variable coefficients and
unbounded electromagnetic potentials, where the kinetic energy part is a long-range
perturbation of the flat Laplacian and the electric (respectively magnetic) potential
can grow subquadratically (respectively sublinearly) at spatial infinity. We prove
sharp (local-in-time) Strichartz estimates, outside a large compact ball centered at
the origin, for any admissible pair including the endpoint. Under the nontrapping
condition on the Hamilton flow generated by the kinetic energy, global-in-space
estimates are also studied. Finally, under the nontrapping condition, we prove
Strichartz estimates with an arbitrarily small derivative loss without asymptotic
flatness on the coefficients.
