  We study quantum corrals on the surface of a topological insulator (TI).
Different resonance states induced by nonmagnetic (NM), antiferromagnetic
(AFM), and ferromagnetic (FM) corrals are found. Intriguingly, the spin is
clearly energy-resolved in a FM corral, which can be effectively used to
operate surface carrier spins of TI. We also show that an observable quantum
mirage of a magnetic impurity can be projected from the occupied into the empty
focus of a FM elliptic corral, while in NM and AFM corrals the mirage signal
becomes negligibly weak. In addition, the modulation of the interaction between
two magnetic impurities in the quantum corrals is demonstrated. These prominent
effects may be measured by spin-polarized STM experiments.
