A local uniqueness theorem for the fractional Schr\'{o}dinger equation on closed Riemannian manifolds

We investigate that a potential $V$ in the fractional Schr\"odinger equation $( (-\Delta_g )^s +V ) u=f$ can be recovered locally by using the local source-to-solution map on smooth connected closed Riemannian manifolds. To achieve this goal, we derive a related new Runge approximation property.
Comment: 6 pages