A minimal disc whose partial Maslov indices are all at least 1 or all at most -1 admits a holomorphic disc of the same image; consequently all minimal discs in CP^m bounded by RP^m are holomorphic.
Lectures on minimal surface theory.arXiv preprint arXiv:1308.3325
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The existence criterion of holomorphic discs for higher $A_\infty$ operations via minimal discs
A minimal disc whose partial Maslov indices are all at least 1 or all at most -1 admits a holomorphic disc of the same image; consequently all minimal discs in CP^m bounded by RP^m are holomorphic.