Nice hand, but please don't flat call a min raise when you hold AA, especially not in that position.
Your check/min raise on the flop screams strength because you are sandwiched between the original aggressor and a third player, so you are in no good position to ever be bluffing there, and if you were bluffing, then you would never make your raise that inviting.
You may get called by a drawing hand, but really you should expect many people to get away from pretty much anything but AQ or maybe KQ. A good opponent folds a draw, even though the pot odds are great, because the board is paired, and he could be drawing dead or hit a "killer out". Much better to just bet out and hope to get someone call or bluff raise with a draw.