Halle Berry's Fiance Olivier Martinez -- Brace Yourself

Halle Berry's fiance Olivier Martinez is on the mend after his brutal fight with Gabriel Aubry on Thanksgiving -- dropping by an L.A. hospital today ... and getting his injured punching hand wrapped in a brace.

As we first reported, Olivier got the better of Gabriel during the fight -- suffering relatively minor injuries in comparison to Gabriel's brutalized face.

An emergency protective order has already been issued against Gabriel -- requiring him to stay 100 yards away from Halle, Olivier, and Nahla -- but Gabriel's rushing to court today to get it lifted.