We derive the BPS equations for D3-branes embedded in AdS_5 X S^5 that preserve at least two supercharges. These are given in terms of conditions on the pullbacks of some space-time differential four-forms. Solutions to our equations are shown to describe all the known giant and dual-giant gravitons in AdS_5 X S^5. We then argue that the configuration spaces of dual-giants can be mapped to non-compact hyperbol
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